Tailor Made Concrete Structures – Walraven & Stoelhorst (eds)© 2008 Taylor & Francis Group, London, ISBN 978-0-415-47535-8

Structural behavior with reinforcement corrosion

V.I. Carbone, G. Mancini & F. TondoloDepartment of Structural and Geotechnical Engineering, Turin, Italy

ABSTRACT: Structural degradation phenomena like reinforcement corrosion in concrete structures imply aconsequent reduction in time of the safety level. Corrosion causes a reduction of the sectional area, ductility andstrength of rebars, of the compressive strength of concrete caused by cracking and consequent concrete spalling,of the bond strength between steel and concrete. The subsequent redistribution of internal stresses inducesa reduction in ductility at ultimate limit state and a variation of the deformational behavior in serviceabilityconditions. In a deteriorated member subjected to bending, concrete in compression reaches suddenly its limitdeformation hindering to develop the full rotation capacity. In the present paper, the effect of a uniform corrosionon reinforcement is analyzed. A numerical model, able to take into account corrosion effects and to describe thestructural behavior of concrete structures, is developed for this purpose.

1 INTRODUCTION

1.1 Corrosion effect on concrete structures

Corrosion of reinforcement in concrete structures isone of the worst and most diffused deterioration phe-nomena. Carbonation of the concrete cover or chlorideattack are the main causes of rebar corrosion. In thefirst case we can see diffused corrosion, while in thesecond both diffused and concentrated effects (pitting)are to be expected. Diffused corrosion will be analyzedin this paper. The damage mechanisms due to corro-sion are mainly: cross section reduction of the bars,induction of swelling stresses in the concrete aroundcorroded bars, bond loss between concrete and steel(Fib (2001)). The compressed zones of members sub-jected to bending crossed by corroded reinforcementsuffer from transverse tensile stresses as written byBertagnoli et al. (2006). The compressive strength ofconcrete has then to be reduced to take into accountthe effect of the transverse stresses. Bond loss oflongitudinal bars is deeply influenced by the degreeof confinement, that concrete cover and stirrups canprovide. The presence of high levels of confinementcan grant good bond conditions even with high cor-rosion, as underlined by Lundgreen & Plos (2006).On the other hand the bond slip law can be deeplysapped with poor confinement and expecially whenlongitudinal cracks along the bars take place. Theaim of this paper is to analyze the effect of the lossof bond in concrete structures due to corrosion ofreinforcement.

1.2 Corrosion effect on bond

A simple reinforced concrete tie subjected to vari-able tensile stress along its length has been studiedto evaluate the effect of corrosion on bond. This tiesimulates the tensed region, controlled by longitudinalreinforcement, situated between two cracks, in a beamsubjected to variable bending moment. The solution ofthis model can be written with the following systemof equilibrium and differential equations where:

In equations (1) to (3) s is the slip, εs and εct are respec-tively the deformations in steel and concrete, σs is thestress in steel, τ is the bond stress, φ is the bar diameter,NL is the axial load, As is reinforcement cross section,Ec and Ac are the elastic modulus and the cross sec-tion of concrete. Figure 1 pictures the actions describedabove.

The longitudinal variation of the load and the dete-rioration of the bond-slip law make the bond stress tobe non symmetric with respect to the mid-section ofthe truss segment between two cracks.

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Figure 1. Actions in a tie subjected to a variable axial load.

The point with nil slip moves towards the end of thesegment with the smaller axial load applied.

If the bond strength drops under a certain level,the sign of the bond stresses τ doesn’t change in thesegment. In this case the reinforcement bars behaveslike an unbonded tendon that slides inside the concreteelement with friction. (Giordano et al. (2007)).

As a consequence the limit situation of completelyunbonded reinforcement has been analyzed to evaluatethe structural behavior of a segment with nil bond-slip law.

2 THE UNBONDED LIMIT MODEL

2.1 Application to a constant moment zone

The structural behavior of a segment of a beam sub-jected to bending where reinforcement is unbondedfrom concrete has been studied by Cairns & Rafeeqi(2003) and by Bertagnoli et al. (2007).

In this situation the hypothesis of equality in defor-mations of steel and concrete is not applicable and thelocal compatibility of the deformations has not to bechecked within the section, but in an integral formwithin the segment.

The equilibrium equations in longitudinal direction(4) and to rotation (5), that have to be verified in eachsection of the segment, need then to be associated toanother equation (6):

This last equation (6) imposes on the whole segmentthe compatibility between the elongations of both

Figure 2. Comparison between concrete strains obtainedwith a fully bonded and a completely unbonded model.

tensed reinforcement and the concrete fiber that islocated at the level of reinforcement.

The overall solution procedure is iterative. At theend the stress inside the bar is constant along the seg-ment, while in each section the strains in concrete arefunction of external actions Ns ed Ms.

If the bending moment and the axial force are con-stant along the segment the solution is the same in eachsection and corresponds to the values reached at theextremities.

2.2 Application to a variable moment region

If the segment of the beam is subjected to a bend-ing moment variable along its length, by the effectof debonding between concrete and steel, the stressin reinforcement will remain constant, whereas thestrains in concrete will change in every section.

The comparison between concrete strains evaluatedwith a fully bonded and a completely unbonded modelare shown in Figure 2.

The maximum compression in concrete (dashedline) is smaller than the one obtained with a full bondmodel (continuous line) in the region of the segmentwhere the bending moment is smaller.

On the contrary the compression in concrete is big-ger that the one obtained with the fully bonded modelin the region of the segment where the bending momentis bigger (M2s > M

1s ).

The loss of compatibility of deformations betweensteel and concrete shown above can be named “Stage3”, in the same way as the uncracked state is named“Stage 1” and the fully cracked state with perfect bondis called “Stage 2”.

This model explains the loss of ductility at ultimatelimit state because of a sudden failure of concrete incompression, as shown by Rodriguez et al. (1996),Mangat & Elgarf (1999) and Bertagnoli et al. (2007).For a better understanding of the experimental evi-dences the beam region to be kept under observation

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Figure 3. Deformation of reinforcement and concrete atdifferent section levels.

that is one where, the maximum strains in materialsare reached. As a consequence one can underline thatbond between steel and concrete plays an importantrole and debonding cannot be disregarded; on the otherend the limit model (complete debonding) explainswell only the extreme level of corrosion. A more gen-eral model able to take into account the bond variationeffect inside the segment is then necessary to completethe approach.

3 THE GENERAL MODEL

3.1 Analysis of a concrete block between twocracks

The numerical model for the evaluation of the behav-ior of members in bending is based on the followingprocedure.

The beam under consideration is divided into seg-ments with a length “srm”, that is to say the distancebetween main cracks in Stage 2, “stabilized cracking”(CEB (1993)). This hypothesis comes from the choiceof analyzing the structural behavior in stabilized crack-ing condition, disregarding the crack formation phase.The regions where the beams have obviously reacheda stabilized crack pattern. Figure 3 pictures the sym-bology used to describe the strains reached at differentlevels of a section under the external actions Ms-Ns.

Tensile strains in concrete are assumed to be linearlyincreasing from the neutral axis to the value εct in cor-respondence of the tensed bars, whose deformationεs cannot be compatible with respect to concrete. Thestrain layout is then composed by three planes, insteadof two as mentioned by Bertagnoli et al. (2006) andCEB (1995) as the strain plane of compressed concreteand tensed steel are different.

Each segment that lies between two consecutivecracks (Figure 4) is analyzed in a first step as dis-jointed from the remaining part of the structure ofcourse remembering to respect in each section inside

Figure 4. External actions acting on a isolated concreteblock.

Figure 5. Mutual effect between the tensed and compressedregion of the block in bending, supposed isolated from thebeam.

the segment the equilibrium to translation and rotationaccording to expressions (4) and (5).

Moreover, as seen for the completely unbondedmodel, the global compatibility (equation 6) isimposed. The boundary conditions at the beginningand at the end of each segment are shared with the twoadjacent ones. Such conditions can be of “Stage 2” or“Stage 3” type.

The shear effect between the compressed part ofconcrete and the tensed chord has to be taken intoaccount in the solution of each segment.

Moreover the tensed tie around reinforcement has avariable profile and is stressed with some eccentricityto its axis. This effect is due to the peculiar shape of thestrains that arise in the tensed concrete, which has lin-ear elastic behavior and stresses varying linearly alongthe depth of the section.

Fracture mechanics effects in beams with morethan the minimum reinforcement have been firstlydisregarded as ultimate conditions were underinvestigation.

Figure 5 shows the compressed and the tensed partof the segment and puts in evidence the shear stressesthat are proportional to the bond stresses between steeland concrete. This phenomenon is due to the fact thattensed steel and compressed concrete manage need tobe connected by means of the bond mechanisms.

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This mutual effect is lost if bond is neglected. Theonly tie between the two parts is then given by equation(3) as seen in the fully unbonded model.

Figure 5 also shows the resultants of the resistingactions for compressed concrete, tensed concrete andtensed reinforcement. For sake of simplicity a beamwith only tensed reinforcement has been chosen.

3.2 Numerical procedure

The solution of the structure is pursued through aniterative procedure. A first trial position of the neutralaxis is supposed and the tensed part is solved as asimple chord. The first approximation of the neutralaxis depth is obtained by linear interpolation betweenthe two values of its depth at the extremely faces ofthe segment.

Solving the tensed chord we get the first trial bondstresses. They give rise to the tangential stresses q,between the compressed and the tensed region, asshown in Figure 5. Such stresses produce in the tensedchord a tension enhancement effect, that is nil at theextremities of the segment and reaches its maximumvalue in correspondence of the point with nil slip,where the sign of the bond stresses changes. The com-pressed chord is, meanwhile, more compressed in themiddle of the segment as a result of the same q stresseschanged in sign. Taking into account the stresses q, weget for each section inside the segment the followingequilibrium equations:

where yct is the distance between the resultant of thetensile stresses in the tensed concrete and the tensedreinforcement.

The new profile of the neutral axis depth is calcu-lated with the equilibrium equations (4) and (5) in thehypothesis of “Stage 3” behavior.

The iterative process ends when convergence isreached on the neutral axis position. At the end theglobal congruence is verified on the entire segment bymeans of equation (6).

If this expression is not verified a new “second trial”value of q, proportional to bond stresses is adopted anda new iteration process to find the neutral axis posi-tion starts. The final configuration of the segment, thatrespects both equilibrium in all the inner sections andcompatibility on the whole length, is obtained whenalso equation (6) is verified. In each inner sectionthe values of Ncc, resultant of compressive stressesNct , resultant of tensile stresses in concrete and Nst,force in the bars, are in equilibrium, but their valuechanges from one section to the other. This can eas-ily explain the function of the stresses q, which areresponsible for the internal actions migration due tothe bond mechanism.

Figure 6. Geometrical and mechanical parameters and loadscheme for beam 31 by Rodriguez et al. (1996).

Figure 7. Concrete block in presence of a constant bendingmoment and an external load equal to 90 kN.

3.3 A block in a constant moment zone

The procedure presented in the previous paragraphsis here applied to a segment of a beam in a zone ofconstant bending moment. The boundary conditionscorresponding to the cracks are obtained with respectto the Stage 2. In Figure 6 geometrical and mechan-ical characteristics of the analyzed beam are shown(Rodriguez et al.(1996)).

For this beam the average distance of cracks isequal to 63 mm and it coincides with the width of theconcrete blocks in which the beam is divided. It is con-sidered a load value of 90 kN that is definitely higherthan cracking one that is about 20 kN. The externalmoment on the block in a constant moment zone is36 kNm, that is about 85% of the maximum resist-ing moment of the section considered. In Figure 7 thedeformation of compressed concrete at the top levelof the section, the steel stress and the slip betweenconcrete and steel are plotted.

From Figure 7 it is possible to appreciate a perfectsymmetry of stresses and deformation. The effect ofbond between concrete and steel reduces in the middleregion of the block the deformation in compression

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Figure 8. Block in a variable moment zone under a level of90 kN.

and the concrete stress; the rebar stress changes in thesame way.

The stress in tension for concrete do not reach highlevels in order to create a new crack in the middle ofthe block. The point with nil slip is then centred withinthe block.

3.4 A block in a variable moment zone

For the same load level the structural behavior of theadjacent block is considered. It is close to the con-stant moment zone: in particular it is assumed that thesection 2 of Figure 5 corresponds to the point of con-centrated external load. In Figure 8 numerical resultsare depicted.

The lack of symmetry is evident from Figure 8; itis possible to recognize the effect of bond in reducingthe deformation of concrete in compression and steelin tension; the point with nil slip moves toward thesmallest external moment

3.5 Interaction between two consecutive blocks

The boundary condition considered during the previ-ous analysis are derived from a fully cracked Stage 2calculus with plane section. As previously mentionedin each crack it is possible to assume a more generalstate of deformation: the Stage 3. In a constant momentzone it is right to assume a Stage 2 condition becauseof symmetry, but when the shear is different from zero,this assumption appear to be incorrect. Moreover theobjective is to extend the results obtained on a singleblock to two consecutive blocks of the beam taking intoaccount the global compatibility. For this reason theequation (6) need to be verified on the entire length ofthe two blocks (from section 1 to section 3 in Figure 9).Besides, using the Stage 2 assumption for section 1 and

Figure 9. Interaction scheme between two adjacent blocks;points of integration for equation (6).

3, different values for the steel stress in section 2 willbe used in order to verify also the internal compatibil-ity between two consecutive points of nil slip (points Aand B). This last condition derives from the necessitythat these two point enclose a portion of the beam inwhich the total amount of the slip between steel andconcrete (6) must be zero.

The stress in section 2 and the value for the tan-gential stresses q for load transfer between steel andconcrete are unknowns, while the two conditions to beimposed derive from the use of (6) between the twocouples of points previously mentioned.

Using this kind of procedure, results depicted inFigure 10 are obtained. The load level is always thesame and corresponds to that one of Figures 7 and8 but the interaction between two adjacent blocks isconsidered now. For the bond-slip law the indicationsof CEB (1993) are assumed taking into account thematerial characteristics depicted in Figure 6. For con-crete in compression Sargin law is assumed, while thestress-strain law in tension is linear-elastic. The rein-forcement is modelled with elastic-plastic hardening.The interaction shows how the peak deformation inthe direction of crack number 2 is increased until thevalue −1.624e−3 with an increment of 5.7%. In orderto obtain this result, at the end of the optimization pro-cess, a reduction of 0.5% in rebar stress is needed.In this way the Stage 2 condition is lost and Stage 3condition take place.

4 THE EFFECT OF REINFORCEMENTCORROSION

4.1 Structural behavior with loss of bond

In Figure 10 are also depicted the numerical results onthe same two blocks for the same load level but with thehalf of bond strength for bond-slip law. From the dotteddashed lines it appears that, because of the bigger slip,caused by the loss of bond, the stress of steel in sec-tion 2 further decreases of 0.8%. The deformation ofconcrete in compression reaches a value of −1.684e−3

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Figure 10. Numerical results for two adjacent blocks; defor-mation of concrete in compression, steel stresses and slip.

with an increase of 9.59% with respect to the classicalsectional solution.

5 CONCLUSIONS

In the analysis of reinforced concrete structures sub-jected to corrosion, an important role is played bybond between steel and concrete. In this work thestructural behaviour of reinforced concrete blocks ofa beam in bending is presented. The effect underexamination is the loss of bond and of the compositeaction between steel and concrete. In order to analyzethis phenomenon the structural behaviour of a blockbetween two consecutive cracks is evaluated. With thesame approach the interaction of two adjacent blocks isstudied; the initial condition of the intermediate crackin Stage 2 is removed in order to attain a local and a

global compatibility. The analysis is performed on aportion of a beam under the 85% of the limit bend-ing moment and subjected to shear. The presence andthe amount of the shear is essential because it deter-mines the macro-slip effect on concrete blocks and thefinal configuration in terms of equilibrium. Thereforethe solution strictly depends on the loading conditions.For full bond strength it appears that the increment indeformation in compressed concrete at the top levelof the section is about 6% while it reaches the valueof 10% when the bond strength is reduced of the half.This explain why the composite effect is granted bythe full bond strength between steel and concrete, butit is reduced when the loss of bond takes place; thereduction of bond in corroded reinforcement is verycommon and this condition produces important effectson the entire structures, because the strain pattern ismodified all over the affected zone. For these reasonsthe structure results to be less ductile and shows pre-mature brittle failures in compression as reported inliterature (Rodriguez et al. (1996)).

REFERENCES

Fib, 2001. Bond of reinforcement in concrete. Fib Bulletinn◦10, Lausanne (CH), Switzerland.

Lundgren, K., Plos, M., 2006.The effect of corrosion on bondin reinforced concrete, European Symposium on ServiceLife and Serviceability., Espoo Finland, 12–14 June.

Giordano, L., Mancini, G., Tondolo, F., 2007. Compor-tamento strutturale di elementi in calcestruzzo armatosoggetti a corrosione. Giornate AICAP, 4–6 October,Salerno.

Cairns, J., Rafeeqi, S. F. A. 2003. Strengthening reinforcedconcrete beams with external unbonded bars: theoreti-cal investigation. Structures and Buildings Vol.156, n◦1,39–48.

Rodriguez, J., Ortega, L. M., Casal, J., Diez, J. M., 1996.Assessing structural conditions of concrete structureswith corroded reinforcement. International congress ofConcrete in the Service of Mankind, Conference n◦5 Con-crete Reparir Rehabilitation and Protection, Dundee, UK,pp. 14.

Mangat, P. S., Elgarf, M. S. 1999. Flexural strength of con-crete beams with corro4ding reinforcement. ACI Struc-tural Journal, Vol.96, n◦1, 149–158.

Bertagnoli, G., Mancini, G., Tondolo, F. 2006. Bond deteri-oration due to corrosion and actual bearing capacity. 2ndfib Congress 5–8 June, Naples.

Bertagnoli, G., Mancini, G., Tondolo, F., 2007. ModellingR.C. structures in presence of reinforcement corro-sion, International RILEM Workshop on Integral ServiceLife Modelling of Concrete Structures 5–6 November,Guimaraes, Portugal.

CEB 1993. Model Code 90; Bullettin 203, Lausanne (CH),Switzerland.

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