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

Advanced numerical design for economical cathodic protectionfor concrete structures

R.B. Polder & W.H.A. PeelenTNO Built Environment and Geosciences, Delft, The Netherlands

F. Lollini, E. Redaelli & L. BertoliniPoliTecnico di Milano, Milano, Italy

ABSTRACT: Concrete structures under aggressive load may suffer chloride induced reinforcement corrosion,in particular with increasing age. Due to high monetary and societal cost (non-availability), replacement is oftenundesirable. Durable repair is necessary, e.g. by Cathodic Protection (CP). CP involves an electrical currentthrough the concrete to the reinforcement from an external anode. The current causes steel polarisation, electro-chemical reactions and ion transport. CP systems are designed from experience, which results in conservativedesigns and their performance is a matter of wait-and-see. Using numerical models for current and polarisationdistribution, CP systems can be designed for critical aspects and made more economical. This paper presentsprinciples and results of preliminary numerical calculations for design of CP systems, applied to protection oflocal damage in bridges (e.g. at leaking joints).

1 INTRODUCTION

Chloride induced reinforcement corrosion is the mostimportant degradation mechanisms in concrete struc-tures (Bertolini et al. 2004). Cathodic Protection (CP)is an effective and widely used method for reinstat-ing corrosion protection(Pedeferri, 1996). CP involvesan electrical current applied from an anode systemthrough the concrete to the reinforcement. Current pas-sage causes polarisation of the steel into the negativedirection, electrochemical reactions at the electrodesand ion transport in the concrete pore solution. Thepolarisation resistance of the steel and the electrolyticresistance of the concrete govern the distribution ofcurrent and potential. With time the polarisation resis-tance will increase due to higher pH and lower chlorideconcentration near the steel and potential and cur-rent distributions will change. Presently, CP systemsare designed without taking this into account, whichresults in conservative designs.With numerical modelsfor current and polarisation distribution, CP systemscan be designed for critical aspects and made moreeconomical. Furthermore, the extent of protection out-side the anode or deeper into the concrete (“throwingpower”) can be predicted. This is illustrated by pre-liminary numerical analysis of a CP system applied topart of a bridge deck (Polder 1998).

2 MODELLING SETUP

2.1 Example structure

The structure for which the CP system was mod-elled consists of two parallel post-tensioned bridgesover the river Dommel near ’s-Hertogenbosch, TheNetherlands. Corrosion was due to de-icing salt leak-age of the joints between the abutments and the deck,see Figure 1. Actual corrosion occurred of transversebars within the first half meter from the joint edge.Deeper lying longitudinal bars and transverse bars fur-ther from the joint did not corrode. A CP conductivecoating anode (AHEAD) was applied over one meterwide from the joint edge. Reference electrodes wereplaced near the reinforcing steel (for protection qual-ity checking) and near the post-tensioning anchors(as a warning for reaching hydrogen evolution poten-tials) according to (EN 12696, 2000). Further detailsare given in (Polder 1998). Numerical simulationswere made using the finite element package COM-SOL Multiphysics. The objectives were to evaluate thedistribution of polarisation and to assess the safety ofthe prestressing steel. Two humidity situations weresimulated by varying concrete resistivity: one valuefor 80% relative air humidity (RH) and one for a RHhigher than 90%, both at 10˚ C. The behavior of steel

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Figure 1. Schematic (longitudinal) cross section of bridgedeck and abutment.

Figure 2. Part of the geometry of the domain (dimensionsin m).

in concrete in both conditions is described using litera-ture data (Redaelli et al. 2006). No temporal variations(active/passive) were considered.

2.2 Numerical model: geometry

The geometry of the real case is quite complex, so inorder to reduce the computation time a 2D model ofa part of the deck’s longitudinal cross section was setup. Numerical simulations carried out on two differentlengths of the modelled part (3 and 5 m) showed thatthe length influenced the results, but the effect wassignificant only for the rebar farthest from the anode,whereas for active bars (under the anode) it was neg-ligible. Therefore it was assumed that a cross sectionwith a height of 0.8 m and 5 m long was representa-tive of the relevant part of the bridge. The transversebars have a concrete cover of 35 mm and are placedat 150 mm centre-to-centre distances, as shown inFigure 2. The three bars closest to the joint, whichwere actively corroding in the real case, have 32 mmdiameter, the rest has 16 mm diameter. The longitudi-nal bars have a diameter of 16 mm and have 100 mmcentre-to-centre distances.

In the 2D model, only transverse bars can be mod-elled in their real position; longitudinal rebars cannotbe modelled as such. However, their presence cannotbe neglected because such bars close to the anode do

influence the current flow. Therefore the longitudinalbars were implemented as a second layer of transverserebars close to the first layer. Each of these rebars wasplaced in between two (outer) transverse bars takingcare to avoid overlapping with the transverse rebars.The real amount of steel was implemented, only thedirection of these bars differs from reality. The diam-eter of these simulated bars was derived from the realsteel surface area, about 0.5 m2 of steel surface areaper m2 of concrete surface area. The longitudinal bars(simulated as transverse bars) had a concrete cover of51 mm.

The bars in the upper side of the deck and thestirrups were modelled by mirroring the bars of thelower side. The presence of post-tensioning ducts andanchors, roughly in the middle of the deck thickness,was taken into account in the same way as the longi-tudinal bars. Taking into account ducts (or anchors) of100 mm diameter placed at 1 m centre-to-centre dis-tances, 5 bars per meter with a diameter of 20 mmwere modelled. As in the real-life case, the anode hada width of one meter starting from the joint edge. Thegeometry of the model used is shown in Figure 2.

2.3 Numerical model: boundary condition

Due to the high electrical conductivity of metals com-pared to that of concrete, the rebars and the anodewere assumed to be equipotential regions, and werenot considered in the domain where Laplace’s equationwas solved. The electrochemical behaviour of activeand passive steel was described through polarisationcurves that were used as boundary conditions in themodel. These curves were expressed as Butler-Volmertype of relations between current density and potentialfor active steel:

and for passive steel

Here i is the normal component of the current den-sity at the steel surface, icorr is the corrosion currentdensity, V is the potential at the concrete side of theinterface, Vcorr is the free corrosion potential, ba and bc

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Table 1. Values of parameters used in equation (1) and (2)(Redaelli et al. 2006).

Condition

Description Symbol Dry Wet

Free corrosion potential Vcorr,A −0.30 −0.36of active steel (V/SCE)

Corrosion current density icorr,A 5 10of active steel (mA/m2)

Anodic Tafel slope ba,A 0.075 0.075of active steel (V/decade)

Cathodic Tafel slope bc,A 0.2 0.2of active steel (V/decade)

Free corrosion potential Vcorr,P +0.1 +0.1of passive steel (V SCE)

Corrosion current density icorr,P 0.1 0.1of passive steel (mA/m2)

Anodic Tafel slope ba,P 10 10of passive steel (V/decade)

Cathodic Tafel slope bc,P 0.2 0.2of passive steel (V/decade)

are the slopes of the anodic and cathodic polarisationcurves. So, in order to describe thoroughly each polari-sation curve, it is necessary to specify four parameters.In principle, each of these parameters may depend onenvironmental factors (wet, dry). The term V − Vcorr ,the polarisation from the corrosion potential due tocurrent flow, is also termed overpotential.

Following previous work (Redaelli et al. 2006), foractive bars it was assumed that the free corrosionpotential was −300 mV/SCE in dry conditions and−360 mV/SCE in wet conditions and the corrosioncurrent density in dry and wet conditions was 5 and10 mA/m2, respectively.

The anodic and the cathodic slopes were takenequal to 75 mV/decade and to 200 mV/decade, respec-tively, identical for dry and wet conditions. For passivebars the parameters in expression (2) were consid-ered independent of environmental factors. Free cor-rosion potential, corrosion current density, anodicand cathodic Tafel slopes were considered equal to+100 mV/SCE, 0.1 mA/m2, 10000 mV/decade (i.e.virtually infinite) and 200 mV/decade, respectively.Table 1 summarises the parameters used in the polar-ization curves.

On the anode, a condition of constant currentdensity was imposed:

Different values of ian were considered (i.e. 10,20, 25 and 35 mA/m2), in order to find the minimumvalue of anode current density that could guarantee acathodic polarisation of 100 mV on the three activelycorroding rebars.

-0.2

-0.18

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0 10 20 30 40

Anode current density (mA/m2)

Ov

erp

ote

nti

al

(V)

wet

dry

Figure 3. Average overpotential on the three active bars asa function of anode current density.

All other boundaries were characterized by insulat-ing conditions:

The model also required specifying the properties ofthe material in terms of electrical conductivity. Sincethe electrical resistivity of the repair mortar used torepair corrosion damage spots had roughly the samevalue as the parent concrete (made with OPC/CEM I),it was assumed that conductivity was constant in space.A value for the electrical resistivity of 1000 � · mwas chosen for dry concrete and of 200 � · m for wetconcrete (Redaelli et al. 2006).

3 RESULTS

Different series of numerical experiments were carriedout, varying the number of the modelled bars and thenumber of corroding rebars.

The first series of numerical experiments was car-ried out for a simplified geometry, with rebars in thelower part of the deck only and without post-tensioningsteel. Models were solved with different values ofanodic current densities, i.e. 10, 20, 25 and 35 mA/m2.As shown in Figure 3, the lowest anodic current den-sity that could polarize the three active rebars by atleast 100 mV was found to be 35 mA/m2. This value ofanodic current density was used also for the rest of thecalculations. The average values of the overpotentialon the steel surface and the steel current densities areshown in Figures 4 and 5, respectively, both for dry andwet conditions. It should be noted that the anode is onlypresent on one meter on the left side. In dry concretethe polarization of the three active rebars was about160 mV. The rest of the rebars below the anode, which

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-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 1 2 3 4 5 6Joint distance (m)

Ove

rpot

enti

al (

V)

wet condition

dry condition

Figure 4. Overpotential on individual bars at differentdistance from the joint; anode is located from 0 m to 1 m.

Figure 5. Current density on bars at different distance fromthe joint.

were passive, had a polarization of 500 mV. The polar-ization of passive rebars decreased with increasingdistance from the anode: for instance in dry concretethe steel polarization is 40 mV at about 1.5 m from theanode and becomes 0 mV at 4 m, whilst in wet concretethe steel polarization is 110 mV at 1.5 m and 44 mV at5 m from the anode.

The cathodic current density was 36–39 mA/m2

(dry) and 33–36 mA/m2 (wet) for the three active bars(see Figure 1) and 41 mA/m2 (dry) and 36 mA/m2

(wet) for passive steel bars under the anode.The potential close to the anode obtained from the

calculation was 0.9V in wet concrete and 2.7V indry concrete; these values can be considered as anestimation of the feeding voltage of the CP system.

Figure 6. Overpotential on bars in dry concrete at differentdistance from the joint.

In the second series of simulations, bars were addedin the upper part or in the middle of the deck (resultsnot shown).

It was found that overpotentials and current densi-ties decreased slightly for bars in the lower part ofthe deck. Placing steel inside the deck (where thepost-tensioning is located) did not have a significantinfluence on potentials and current density of the lowersteel.

Further simulations were carried out with a com-plete set of rebars in the lower and upper deck andpost-tensioning in the middle, as shown in Figure 2.

For the third series of simulations the number ofactive transverse rebars was varied. From the joint edgestep-wise 3, 5, 8 or 10 bars were assumed to be activelycorroding. Bar #8 is located at a distance of 0.916 mfrom the joint and thus is the last bar directly under theanode; bar #10 is well outside the anode.

Figures 6 and 8 show the overpotential for active andpassive steel for varying numbers of corroding bars indry and wet concrete, respectively. Figures 7 and 9illustrate the current densities on active and passivesteel rebars for dry and wet conditions, respectively.

In general and in particular if high polarization isprovided by a CP system, overprotection of the post-tensioning steel, ducts and anchors must be carefullyregarded due to the possibility of hydrogen evolution(and subsequent embrittlement).

The absolute potentials of steel versus saturatedcalomel electrode at the position of the post-tensioningwere calculated to check this possibility. The modelwas used to calculate the potentials of the post-tensioning steel for a varying number of active rebarsfor dry and wet concrete. The calculations showed thatthe most negative absolute potential reached was about−150 mV/SCE in dry conditions and −220 mV/SCEin wet conditions. They did not significantly depend

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Figure 7. Current density on bars in dry concrete at differentdistance from the joint.

Figure 8. Overpotential on transverse bars in wet concrete,at different distance from the joint.

on the number of actively corroding bars. These poten-tials are well into the safe range from the point of viewof hydrogen evolution, which occurs at potentials morenegative than −900 mV/SCE (EN 12696, 2000).

4 DISCUSSION

As mentioned above, the potential calculated throughthe numerical simulations allows calculating the over-potential which is the polarisation of the steel due tocurrent flow. Assuming that this polarisation will relaxto zero in the normal testing period of four to 24 hoursafter current switch-off, the “overpotential” could beinterpreted as “depolarisation”. A value of 100 mVor more was taken as an indication of protection, inaccordance to (EN 12696, 2000).

Figure 9. Current density on transverse bars in wet concrete,at different distance from the joint.

In the first (preliminary) set of numerical experi-ments, a cathodic polarisation of 100 mV for activelycorroding bars in wet concrete was obtained with ananodic current density of 35 mA/m2; lower values ofanodic current densities resulted in polarisation valueslower than 100 mV, which was considered inadequateto protect active rebars. Much higher cathodic polar-isation values were obtained on passive bars, about500 mV for the rebars below the anode and 110 mVfor rebars at 1.5 m from the anode. In dry concrete thesteel polarization was about 160 mV for active rebarsand 510 mV for passive rebars below the anode, and40 mV at 1.5 m from the anode. The current densityon the rebars (active and passive) below the anode was37–40 mA/m2. Compared to measurements in thefield, these calculated current densities seemrather high.

The second set of simulations showed that addingsteel inside the modelled cross section or on the oppo-site side of the deck from the anode, did not have a largeinfluence on the current to the steel immediately belowthe anode. Overpotentials reached at steel inside thecross section (e.g. post-tensioning steel) were mildlynegative.

In the third series, the number of corroding barswas varied in the lateral direction with respect to thefixed anode surface. Numerical simulations showedthat actively corroding bars are protected as long asthey are below the anode; active rebars outside theanode (even a few centimeters) received less currentand were less polarised; the protection falls off stronglyfrom the edge of the anode. Passive bars were wellpolarised, more or less independent of the number ofcorroding bars, also outside the anode (as with the firstseries), in particular in wet concrete.

In a general sense, it appears that current distribu-tion in the concrete is under ohmic control.

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The steel current densities obtained with the simu-lations are higher than would be normally expected in aCP system, typically 10 mA/m2. This could be causedby several factors, such as assuming incorrect steelpolarisation curves or boundary condition at the anode,incorrect values of concrete resistivities, making sim-plifications in the geometry or incomplete taking intoaccount other effects.

Geometrical simplifications cannot be the maincause, as the real amount of steel and its approxi-mate position were taken into account. Measurementson concrete resistivities in various climates suggestthat more or less correct values were used. Othersteel polarisation curves could be used, e.g. con-sidering different values of corrosion potential andcurrent density. However, it is hard to obtain polari-sation curves from real cases and our estimate is thebest guess we can make now. The most importantfactor that was not taken into account is the benefi-cial effect of the current itself: negative polarisationby CP is aimed at reinstating the passivation of thesteel. Consequently, the polarisation curve of activesteel should shift towards that of passive steel. Fulltreatment of this effect requires better insight intocurrent- and time-dependent active/passive transitionsof steel in concrete. It should be noted that for the highcurrent density applied, passive steel showed polari-sation values of about 500 mV. This suggests that areduced corrosion rate due to current assisted passi-vating effects would sharply increase the polarisation.This would allow the current density to be reduced sig-nificantly. In practice, fixed voltage driven CP systemsusually show a relatively high current density at start-up; then a strong reduction of the current in a matterof days to weeks. Further work is needed on this issue.

5 CONCLUSIONS

A finite element model was set up for cathodic pro-tection of steel in concrete, taking into account theelectrochemical properties of steel (active, passive)and concrete (dry, wet) as fixed values. The geometryof part of a bridge deck was simplified in 2 dimen-sions, including individual bars with realistic surfaceareas and positions; the anode covered only part of theunderside of the simulated bridge deck, where someof the rebars were actively corroding. Local potentialsand current densities were calculated using Butler-Volmer type steel polarisation behaviour. The amountof steel polarisation from the free corrosion poten-tial (overpotential) is taken to represent the amount ofdepolarisation that is measured when the CP currentis switched off, which is the usual way of checking thequality of protection.

Applying an anodic current density of 35 mA/m2,100 mV polarisation or more (indicating protection)was obtained for corroding bars under the anode in wetconcrete; and for passive bars outside the immediatevicinity of the anode, both in lateral direction alongthe deck and deeper inside the cross section of thedeck. Actively corroding bars would be protected onlyif they are under the anode. Steel inside the cross sec-tion would not reach very negative potentials that couldallow hydrogen evolution (which should be avoided forprestressing steel).

Compared to practical CP systems after some timeof operation, the current density seems quite high.A reasonable explanation is that the time-dependentbeneficial effects of polarisation and current flow areneglected. Further work into modeling of passivatingeffects of CP with time is necessary. It is also foreseenthat field data will be used to validate the model.

ACKNOWLEDGEMENTS

A short term scientific mission was carried out byDr. Elena Redaelli in the framework of COST Action534 “New materials and systems for prestressed con-crete structures” (COST 534-1537) in June 2005 atTNO, which laid the foundation for this work.

The financial support of the Delft Cluster(Delft Cluster project CT02.30 “Smart Sustain-able Management of Concrete Structures”) andTNO/TUDelft knowledge centre Durable ConcreteStructures (DUCON) for Federica Lollini’s stage atTNO during 2007 is gratefully acknowledged.

REFERENCES

Bertolini, L., Elsener, B., Pedeferri, P., Polder, R.B. 2004. Cor-rosion of Steel in Concrete: Prevention, Diagnosis, Repair,Wiley-VCHVerlag GmbH & Co. KGaA,Weinheim, ISBN3-527-30800-8, 392 pp.

EN 12696, 2000, Cathodic protection of steel in concrete.Pedeferri, P., 1996, Cathodic protection and Cathodic preven-

tion, Construction and Building Materials, Vol. 10, (5),391–402.

Polder, R.B., 1998, Cathodic Protection of Reinforced Con-crete Structures in The Netherlands – Experience andDevelopments, in: Corrosion of reinforcement in con-crete – monitoring, prevention and rehabilitation, Papersfrom Eurocorr’97, Mietz, J., Elsener, B., Polder, R.,Eds. The European Federation of Corrosion Publicationnumber 25, The Institute of Materials, London, ISBN1-86125-083-5, 172–184.

Redaelli, E., Bertolini, L., Peelen, W., Polder, R., 2006,FEM-models for the propagation of chloride induced rein-forcement corrosion, Materials and Corrosion, Vol. 57,(8), 628–635.

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