Development of a numerical simulation model considering ...download.xuebalib.com/xuebalib.com.4230.pdf · Especially in Impressed current cathodic protection (ICCP) systems the discretization

Materials and Corrosion 2016, 67, No. 6 DOI: 10.1002/maco.201608832 621

Development of a numerical simulation modelconsidering the voltage drops within CP anodesystems in RC structures

Dedicated to Dr. J€urgen Mietz on the occasion of his 60th birthday

C. Helm* and M. Raupach

Cathodic protection (CP) can be used as an electrochemical repair andprotection method for reinforced concrete (RC) structures. It often providestechnical and economic advantages versus conventional repair methods fornumerous boundary conditions. Hence, the application of CP is recentlyconsidered for repair measures with complicated arrangements ofreinforcement or geometries. In these cases, the common design guidelines andcriteria for CP applications may fail or lead to erroneous results. The numericalprediction of the current and potential distribution within the structure canthen be used for design purposes. The modeling procedure for CP differs fromthose for galvanic corrosion by existence of an additional CP anode system.Especially in Impressed current cathodic protection (ICCP) systems thediscretization of the CP anode has a significant impact on the modelingprocedure and its results. In this paper, a novel approach is proposed andcompared to existing approaches for relevant parameters including concreteresistivities by means of parametrical studies.

1 Introduction

Cathodic protection is a common repair method for reinforcedconcrete structures affected by chloride-induced macro cellcorrosion. Its effectiveness has been proven by numerousscientific research projects as well as case studies. However, notall knowledge from these studies has expanded into practice. Theline of action in the design and maintenance of today’s CPsystems applied on reinforced concrete structures is stillgoverned by empirical calculations and criteria. Although thesemethods work fine for common applications, there is anincreasing demand to use CP for protection of unusualgeometric arrangements of concrete and rebar, e.g., in the areasof joints or with difficult access. In these cases, numericalsimulations of the current and potential distribution withinreinforced concrete members during CP can be used to predictfeasibility.

C. Helm, M. Raupach

Institute of Building Materials Research, Conservation and Polymer

Composites, RWTH Aachen University, Schinkelstr.3, 52062 Aachen

(Germany)

E-mail: [email protected]

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While the simulation of galvanic CP, e.g., with sprayed ordiscrete zinc anodes, does not differ much from the simulationof any other corrosion process in RC, ICCP systems require amore complex approach. Different discretizations of impressedcurrent anode systems from varying authors are being presentedbelow. The underlying assumptions as well as their impact on theresulting current and potential distribution are being discussed.Afterwards a novel approach will be presented. Finally, allselected approaches will be compared within a numerical studyin order to determine their applicability for certain compositionsof geometry, concrete resistivities, or anode materials.

2 Theoretical backgrounds

2.1 Corrosion of steel in concrete

Steel in concrete is protected against corrosion due to the highlyalkaline pore solution that leads to the formation of a densepassive layer on the steel surface. This layer prevents the anodicdissolution of iron. To initiate corrosion, a breakdown of thispassive layer is necessary. This can either be caused by the loss ofalkalinity because of carbonation or by the ingress of chlorides.

© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Figure 1. Scheme of macro element type corrosion of steel in concrete

622 Helm and Raupach Materials and Corrosion 2016, 67, No. 6

Carbonation-induced corrosion is normally characterized by auniform distribution of anodic and cathodic areas on the steelsurface and slow loss of cross section. Corrosion induced bychlorides that have either been added to the concrete mixture toaccelerate the hardening or that penetrated the concrete coverfrom the surface (e.g., de-icing salts, seawater in marineenvironment, or as a result of PVC burning) is more dangerous.It is characterized by a pitting kind of corrosion, where anodicand cathodic areas are spatially separated. This can cause a rapidloss of cross section and high corrosion rates because of a highcathode to anode area ratio. The driving force of the corrosionprocess is the potential difference between the anode andcathode; in this case, the actively corroding rebar and the rebarthat still remains passive. Between these areas a macro cell isformed, see Fig. 1.

2.2 CP of steel in concrete

CP is an electrochemical repair method for RC structuresaffected by chloride-induced corrosion. The main advantageversus other repair methods is the option to leave concrete that iscontaminated beyond the critical chloride threshold level inthe structure, as long as no significant cracking or spallinghas occurred. The corrosion protection of the reinforcement isachieved by the input of an external protection current viaadditional CP anodes. This current is meant to polarize thereinforcement in cathodic direction in order to suppress theanodic dissolution of iron and to level the potential differencesbetween active and passive steel surfaces. The application of CPhas usually to remain for the entire residual service life.However,experience from CP installations shows that it might be possibleto switch them off after several years, depending on the specificconditions. On the long term additional beneficial effects,particularly the extraction of chlorides and realkalisation in thevicinity of the rebar occur [1–4]. The procedure itself as well asthe criteria for verification of a sufficient protection for thereinforcement are described in Ref. [5].

As the polarization of the reinforcement is vital for theeffectiveness of CP, calculations have to be made regarding theestablishing of protection zones and current requirements [6].Themethods used for this process aremainly based on empiricaldata and practical experience as well as cost effectiveness. Onlythe ohmic drop within the anode material itself is taken intoaccount. Numerical simulation of CP systems provide a novelopportunity to optimize the layout process.


2.3 Numerical modeling of RC corrosion

Any arrangement of electrically connected anodes and cathodesinside an electrolyte will result in a certain distribution ofpotentials on the electrode surfaces. This causes the formation ofa spatially variable electrical field inside the electrolyte. Theresulting current densities of the anodic and cathodic reactionscan then be assessed by use of the following boundaryconditions [7]:

The potential distribution inside the concrete can bedescribed by Laplace’s Equation (1), assuming that the electrolyteis homogeneous

r2U ¼ 0 ð1Þ

The current flow in any direction results in

Ixj ¼ s � rE ð2Þ

The total current density for any part of the electrodesurfaces can be calculated via Ohm’s law

Is ¼ s � @E@n

ð3Þ

where E is the potential, r2 is the Laplace operator, Ixj is thecurrent flow in direction xj, r is the Nabla operator, and Is isthe total current density.

s ¼ 1r

ð4Þ

where r is the resistivity.The vector normal to the potential gradient has to be zero at

all isolating surfaces

@E

@n¼ 0 ð5Þ

Due to electro neutrality, the sum of all currents inside thesystem has to be zero as well

Z

F

idA ¼Z

Fa

iadAþZ

Fc

icdA ¼ 0 ð6Þ

The current density is a function of the electrode potentialand can be described by a polarization curve for each electrode

ia ¼ f aðEaÞ ð7Þ

ic ¼ f cðEcÞ ð8Þ

where ia is the current density of the anodic reaction, ic is thecurrent density of the cathodic reaction, Ea is the anodicpotential, Ec is the cathodic potential, fa is the anodic polarizationcurve, and fc is the cathodic polarization curve.

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igure 2. Scheme of an impressed current CP system with embeddeditanium mesh anodes

Materials and Corrosion 2016, 67, No. 6 Numerical simulation of CP anode systems in RC structures 623

The equations above allow for an analytical calculation ofLaplace’s equation for any given set of linear polarization curves.In case of non-linear polarization behavior, numerical methodshave to be applied.

A common method to assess the respective polarizationproperties expressed by Equations (7) and (8) is the realization ofpotentiodynamic experiments, see Section 3. The implementa-tion in the numerical calculations is usually achieved by fittingthe results with the Butler–Volmer equation:

i ¼i0 � exp 2:3�h

ba

� �� exp �2:3�h

bc

� �h i

1þ i0ilim;ox

� exp 2:3�hba

� �� i0

ilim;redexp �2:3�h

bc

� � ð9Þ

where i is the current density on steel surface, i0 is the exchangecurrent density, h is the over potential (E�E0), E is the potential,E0 is the free corrosion potential, ba is the anodic Tafel slope, bc isthe cathodic Tafel slope, ilim,ox is the limiting current density ofthe anodic reaction, ilim,red is the limiting current density of thecathodic reaction.

For systematic use of numerical modeling of macrocellcorrosion in RC structures, see, e.g., Ref. [8].

2.4 Numerical modeling of CP

The basic principles of numericalmodeling of CPare the same asthose for galvanic corrosion. Equations (1)–(8) remain un-touched. The main difference is the addition of the CP anodesystem and the way it is respected in the model. Therefore, thediscretization of the CP anode depends strongly on the nature ofthe anode system to be represented. In the following, differentapproaches for the numerical consideration of CP anodesystems are given.

2.4.1 Galvanic CP

Early CP applications on RC structures where realized by use ofgalvanic anode systems, e.g., discrete, sprayed, or adhesive zincanodes [9,10]. The cathodic polarization of the rebar is thenachieved by use of CPanodematerials which showmore negativefree corrosion potentials in alkaline environment than the activerebar. The protection current density in this case can also bedescribed as a function of the potential:

icpa ¼ f cpaðEcpaÞ ð10Þ

where icpa is the current density of the CP anode and Ecpa is theCP anode potential.

Hence, numerical modeling of galvanic CP does not requireany systematic changes in the modeling process except theaddition of the CP anode system. As the protection current iscreated by active corrosion of the CP anode, the service life islimited either by complete consumption of the anode material,the formation of non-conductive oxide layers in the anodeconcrete interface or bond loss. Furthermore, the driving voltageof galvanic CP systems is determined by the difference betweenthe free corrosion potentials of the rebar and the CP anodesystem. Due to these reasons, the applicability for RC structures

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is limited. Today, the majority of CP installations are realized byICCP.

2.4.2 ICCP

In contrast to galvanic CP, ICCP anode materials do not need toprovide negative free corrosion potentials themselves. Thedriving voltage is created by use of an external rectifier, see Fig. 2.

This method allows for the use of noble anode materials.Themost common CP anodematerial today ismixedmetal oxide(MMO) coated titanium. It is available in multiple forms such asmeshes, wires, or drilled core anodes. MMO is electrochemicallyinert and very durable under anodic polarization. If therequirements for the CP system are less demanding, carbon-based anode systems are used. The most common types ofanodes are conductive coatings or mortars [11,12] or embeddedmeshes [13–15]. Due to their non-inert nature, the performanceof these anodes is inferior to MMO anodes, but they can provideeconomic or technical advantages for certain circumstances.

For the consideration of ICCP anodes in a numerical model,different approaches have beenmade. These approaches differ intheir complexity and each one provides certain advantages andlimitations. Basically three different methods can be identified.

2.4.2.1 Constant potential method: The simplest approach is theuse of constant potentials. In this approach, the CP anode isconsidered to be a boundary of the concrete domain, analogousto the active and passive rebar. Then a constant potential, whichis more negative than the free corrosion potential of the activerebar, is assigned to the boundary in order to create the protectioncurrent. The magnitude of the protection current can only becalculated from the result as the surface integral over the CPanode surface. Hence, a parametric sweep for the anode potentialhas to be carried out. Latest finite element method (FEM)software supports this approach with particular parametricsweep functions. A disadvantage of this method is that the actualdriving voltage needed is initially unknown. Therefore, a lotof calculations have to be done, but due to the constantboundary condition for the CP anode, the expenditure of time is


Figure 3. Exemplary current and potential distribution for the“constant potential method” igure 4. Exemplary current and potential distribution for the

onstant current method”


usually acceptable. This approach has, for e.g., been used inRefs. [1–3,16–18].

Two basic assumptions aremade in this approach. First, thateach surface element defined as CP anode has the same potentialand hence the polarization resistance of the anode is negligible.Second is, that the anode polarization is independent of itsposition, implying that the resistivity of the anode itself isnegligible.

In Fig. 3, an exemplary potential distribution at a CP anodesystem is given for a simple geometry. A single rebar with adiameter of 14mm is embedded in a concrete with a bulkresistivity and concrete cover thickness of 40mm. The CP anodesystem is located on the top side. Only half of the specimen ispictured, as symmetry is used. The equipotential lines presentthe voltage drop within the system whereas the streamlinesindicate the path of the current flow. The streamlines arepositioned by magnitude. The closer the distance between twostreamlines, the higher is the local current density. Equidistantstreamlines indicate a homogenuous current flow.

2.4.2.2 Constant current method

The second approach is quite similar to the constant potentialapproach. In this case, a mean protection current is calculatedaccording to Equation (11).

iiccpa ¼ I iccpaAiccpa

¼ const: ð11Þ

where iiccpa is the current density of the ICCP anode or protectioncurrent density, Iiccpa is the total current of the protection zone,and Aiccpa is the protection zone area.

The protection current is then again applied as a boundarycondition in form of an outward current flow. An example forthis method is given in Fig. 4.

The use of this approach is very convenient, as for anyprotection current applied only one solution exists. This resultsin short calculation times and the method can be used, e.g., tocheck compliance of rebar polarization with Ref. [5] for different


F“c

protection currents. Yet, there is only few reference about thisapproach given in the literature. This may result from theunderlying assumptions. Contrary to the constant potentialapproach, this CP anode formulation allows for a locally varyingpotential distribution, while the local current density is keptconstant. The conductivity of the anode system itself as well asthe polarization resistance is again being neglected.

Whether the basic assumptions described above areapplicable or not for a variety of input factors will be discussedin Section 6.

2.4.2.3 Potential sweep method: A more sophisticated approachfor the ICCP anode in numerical calculations is achieved by useof the potential sweep method. The main advantage versus theconstant potential or current approach is the opportunity toconsider the respective polarization resistance of any givenanode material. The polarization properties of the ICCP anodehave to be determined by polarization testing and to beanalytically fitted subsequently, e.g., by use of Equation (9).The non-linear polarization resistance is given for any presentover-potential h as the related slope of the polarization curve. Tocarry out calculations for a given protection current, the freecorrosion potential of the anode material E0,iccpa needs to beshifted to more negative values until the integral of the totalcurrent passing through the protection zone area Aiccpa matchesthe desired level of protection current. The difference of E0,iccpaand the shifted potential Eiccpa can be interpreted as the integraldriving voltage for the simulated ICCP system. An exemplarypotential distribution for a conductive coating anode system isgiven in Fig. 5.

Similar to the constant potential method, a sweep of theanode potential is necessary in order to determine the actualdriving voltage. Therefore, a lot of calculations have to be done,whereby in this case, the CP anode system is reflected by anonlinear boundary condition of the concrete domain. Especiallythe simulation of larger three-dimensional structures is a timeand disc space consuming procedure using this method.

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Figure 5. Exemplary current and potential distribution for the“potential sweep method”

Figure 6. Exemplary current and potential distribution for the “sheetresistance method”


Furthermore, the variation of any input parameter, e.g., concreteresistivity, requires a complete restart of the procedure. Theapproach has been used in several publications [3,19–21]. Unlikethe consideration of the polarization resistance, the negligence ofthe anodes resistivity is not solved by this approach. Theapplicability has, therefore, also to be discussed for certainboundary conditions, see Section 6.

2.4.2.4 Sheet resistance method: The novel approach proposedby the authors aims on the consideration of the conductivity ofthe CP anode material as well as its respective polarizationresistance. The approach is intended to be used for thesimulation of surface applied anode systems. The impact ofthe sheet resistance resulting from the anode materialsconductivity and thickness is suspected to be more explicitthan for discrete anodes.

The application of this method requires the addition of asecond domain besides the concrete. The purpose of this domainis to reflect the anodematerial and it has to be added to themodelaccording to its actual geometrical arrangement, in case ofsurface applied anode systems this is usually on the top side. Forconductive coating anode systems, the materials resistivity¼riccpa and thickness¼ diccpa can be used directly, either fromexperiment or the manufacturer’s data sheets.

The topside of the CP anode is defined as insulatingsurface, see Equation (5). If symmetry is used regarding thearrangement of the primary anodes, the same applies for onelateral end.

On the remaining end, the protection current is induced asan inward current flow and the current density has to be adjustedto the anode thickness by use of Equation (12).

if eed ¼ I iccpadiccpa

¼ iiccpa � Aiccpa

diccpað12Þ

where ifeed is the current density on the primary anode/bulkanode material interface.

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Following, the polarization curves are applied to the anode/concrete interface in form of a contact impedance

iiccpa ¼ 1rcontact

� ðE1 � E2Þ ð13Þ

where rcontact is the reciprocal derivation of the polarization curveof the CP anode system, E1 is the potential on the anode domainside of the interface, and E2 is the potential on the concretedomain side.

1rcontact

¼ f cpaðEcpaÞ @

@Eð14Þ

With this formulation, the local voltage drop in the anode/concrete interface is dependent on the local current flow, whichis an alternative consideration of the polarization resistance ofthe CP anode.

Figure 6 shows an exemplary potential distribution in theconcrete/anode interface.

This novel approach now allows for the realisticconsideration of both, the anode systems conductivity aswell as its respective polarization resistance. Furthermore, theapproach is more convenient as the potential sweep method,as only one solution exists for every protection current density.This allows to conduct multiple parametric studies in onecalculation [22].

3 Experimental

Prior to the numeric calculations, the required input data had tobe assessed. Within this study, the respective polarization curvesof the CP anode and the active rebar had to be determined bymeans of polarization testing. Therefore, potentiodynamicmeasurements were conducted.


igure 7. Specimen for the determination of the polarization propertiesf conductive coatings


Fo

Table 1. Concrete mix

Binder(�)

Binder content(kg/m3)

w/b-ratio(�)

Chloride content(M.-%/b)

OPC 275 0.65 3

3.1 Conductive coating

The specimen setup is given in Fig. 7.The counter electrode was made from MMO mesh in

order to achieve a homogeneous electrical field. The coatingserved as the working electrode. The measurements weredone versus a cast in MnO2 reference electrode. A feed rate of0.0333mV/s was used. Within this study, the polarizationbehavior of a commercially available conductive coating on anOPC (CEM I) concrete was assessed. The specimen was storedand tested at 20 8C/80% r. h.. The concrete mix was chosen toreflect a typical on site concrete, found in an aged structureaffected by chloride-induced macro cell corrosion and is givenin Table 1.

The test was conducted up to a current density of 20mA/m2

with respect to the concrete surface. After each run, an instant-offmeasurement was conducted in order to determine the ohmicdrop, which was then eliminated calculative from each reading.The dimensions of the specimens were 25� 25� 9 cm3.

3.2 Active reinforcement

The input data for the active rebar have been determined analogto Section 3.1 on macro cell specimen with the same concretemix, see Table 1.

Table 2. Fit parameters for conductive coating and active rebar

Electrode (�) i0(A/m2)

E0 vs. MnO2(V)

Conductive coating 0.0017 �0.2Active rebar 0.0055 -0.526


3.3 Fitting of polarization curves

To integrate themeasured polarization behavior of the electrodesinto the numerical model, an analytical description is needed.The numerical model presented below contains two differentelectrode types, the conductive coating (CP anode) and activerebar. For both types, the Butler–Volmer Equation (9) was used tofit the respective polarization curves.

The fit parameters were chosen to approximate the readingsas good as possible within the expected potential range duringthe application of CP. This may lead to a suboptimal fitting ofother regions as well as parameters outside the theoretical limits.The parameters chosen for the calculations below are given inTable 2. A visualization of the measured data as well as therespective fit functions is given in Fig. 8.

4 Numerical modeling

The numerical modeling within this work has been carried outby use of the FEM software Comsol Multiphysics 5.0. In thefollowing section, the chosen geometry as well as the relevantinput parameters are presented.

4.1 Geometry

For this study, a two-dimensional approach has been chosen. Thepurpose of the selected geometry is to reflect a smaller part of adeck-like structure. A single rebar layer with 15 cm spacing anddiameters of 10mm has been integrated. The concrete cover hasbeen set to 20mm. The whole rebar surface is considered to be inactive corrosion state. For the CP anode, a surface appliedarrangement has been set. The modeling of the sheet resistancemethod required an additional layer on top of the specimen aswell as a primary anode system for the current input on the farleft side, see Fig. 9.

Considering symmetry, the model then reflects a conductivecoating ICCP system with 1.5m spacing of the primary anodes.

4.2 Input parameters

The average current density of 5mA/m2 with respect to theconcrete surface has been selected to result in realisticpolarizations of the rebar for the present geometry and rebarcontent in previous studies. Therefore, this value was useddirectly (constant current or sheet resistance approach) or aimedat (constant potential or potential sweep) in all cases. The bulkconcrete resistivity was varied, starting at 500Ωm. The polariza-tion properties of the rebar given in Table 2 were applied by use ofEquation (9) defined as current flow on all rebar surfaces.

ba(V/dec)

bc(V/dec)

ilim,ox(A/m2)

ilim,red(A/m2)

0.34 0.04 0.045 �1.20.15 0.265 1.0 �1.0

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0

2

4

6

8

10

12

0 0.15 0.3 0.45 0.6 0.75

curr

ent d

ensi

ty c

p an

ode

[mA

m-2

]

x [m]

concrete resistivity 100 Ω m

constant potential constant currentpotential sweep sheet resistance

igure 10.Calculated anode current density for a concrete resistivity of00Ωm for different CP anode discretizations

0.01

0.1

1

10

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

curr

ent d

ensi

ty [m

A m

-2]

potential vs. MnO2 [V]

polarization properties

conductive coating

Butler-Volmer-fit

active reinforcement

Figure 8. Polarization curves of conductive coating and activereinforcement


The CP anode systems were applied individually accordingto Section 2.3. For the potential sweep and sheet resistanceapproaches, the data given in Table 2 were processed according totheir respective description, see also Section 2.3. The conductiv-ity of the coating material as well as its thickness, see Fig. 9, wastaken from manufacturer’s data sheets. For the conductivity, themaximum value of 0.1Ωm was used, in order to simulate themaximum effect of this parameter for acceptable quality ofapplication.

4.3 Parametric study

The opportunity to carry out parametric studies to assess theinsulated impact of any geometric or electrochemical parameteris one of the main purposes of numerical studies for theprediction of the current and potential distribution of CP in RC.The scope of this paper is to compare the impact of differentdiscretizations of CP anode systems. The various approachesdiffer from each other primarily in the negligence or allowance ofpolarization and sheet resistances. Earlier work has shown thatthe magnitude of the concrete resistivity has huge effect on theimpact of the polarization resistivities [4].

Hence, it has been chosen to vary the bulk concreteresistivity from 100Ωm, reflecting water saturated conditions, to500Ωm for moderate exposure, 2 kΩm for fairly dry and

igure 9. Geometry of the numerical model, “sheet resistance method”
F
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10 kΩm for very dry conditions. The results of the differentapproaches are given in the next section.

5 Results

In the following section, the results of the numerical calculationsare presented. Figures 10–13 show the distribution of theprotection current in the anode/concrete interface for increasingbulk concrete resistivities. On the X-axis, the position withrespect to the rebar is given. 0m is the position of the primaryanode (sheet resistance method), at 0, 0.15, 0.30, 0.45, 0.6, and0.75m rebar is positioned under the CP anode. The averageprotection current is 5mA/m2 in every case.

Figures 14–17 show the distribution of the localized anodepotential in the anode/concrete interface analogous to thecurrent densities presented above. This value can also not bemeasured in practice as it would require an infinite number ofinstant offmeasurements in the concrete/anode interface, whichis usually not accessible for reference cells due to surfaceprotection systems.

Finally, the impact of different discretizations of the CPanode system on the calculated polarization of the rebar is given


0

2

4

6

8

10

12

0 0.15 0.3 0.45 0.6 0.75

curr

ent d

ensi

ty c

p an

ode

[mA

m-2

]

x [m]



Figure 11. Calculated anode current density for a concrete resistivity of500Ωm for different CP anode discretizations

0

2

4

6

8

10

12

0 0.15 0.3 0.45 0.6 0.75

curr

ent d

ensi

ty c

p an

ode

[mA

m-2

]

x [m]

concrete resistivity 2 kΩ m


Figure 12.Calculated anode current density for a concrete resistivity of2 kΩm for different CP anode discretizations

-1.2

-1.1

-1

-0.9

-0.8

-0.7

-0.6

0 0.15 0.3 0.45 0.6 0.75

pote

ntia

l cp

anod

e [V

]

x [m]



igure 14. Calculated anode potential for a concrete resistivity of00Ωm for different CP anode discretizations

-1.2

-1.1

-1

-0.9

-0.8

-0.7

-0.6

0 0.15 0.3 0.45 0.6 0.75

pote

ntia

l cp

anod

e [V

]

x [m]



Figure 15. Calculated anode potential for a concrete resistivity of500Ωm for different CP anode discretizations


in Fig. 18 for the water saturated case. Figure 19 presents theresults for very dry conditions.

6 Discussion

Looking at the current density distribution at the anode/concreteinterface, given in Figs. 10–13, it is obvious, that all anode

0

2

4

6

8

10

12

0 0.15 0.3 0.45 0.6 0.75

curr

ent d

ensi

ty c

p an

ode

[mA

m-2

]

x [m]



Figure 13. Calculated anode current density for a concrete resistivity of10 kΩm for different CP anode discretizations


F1

discretizations other than the constant current approach show arather high scatter from the mean anode current density, whichis obviously affected by the positioning of the rebar in theunderlying concrete. This can be attributed to the concreteresistivity. The constant current approach is resulting in ahomogeneous current density distribution by definition, whilethe constant potential approach results in a concrete resistivity

-2

-1.9

-1.8

-1.7

-1.6

-1.5

-1.4

-1.3

-1.2

-1.1

-1

0 0.15 0.3 0.45 0.6 0.75

pote

ntia

l cp

anod

e [V

]

x [m]



Figure 16. Calculated anode potential for a concrete resistivity of2 kΩm for different CP anode discretizations

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-5

-4.8

-4.6

-4.4

-4.2

-4

-3.8

-3.6

-3.4

-3.2

-3

0 0.15 0.3 0.45 0.6 0.75

pote

ntia

l cp

anod

e [V

]

x [m]



igure 17. Calculated anode potential for a concrete resistivity of0 kΩm for different CP anode discretizations


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120

140

160

180

200

220

240

0 0.15 0.3 0.45 0.6 0.75

pola

rizat

ion

[mV]

x [m]


constant potential constant current

potential sweep sheet resistance

Figure 18. Calculatedminimum polarization of each rebar for differentanode discretizations for a concrete resistivity of 100Ωm

controlled current density distribution without exception, as itneglects any polarization resistivities on the anode side.

As the shape of the electrical field itself is not affected bya change in concrete resistivity, the calculated current densitydistribution for the constant current method is more or lessunchanged for all tested concrete resistivities. The changes inthe vicinity of the rebar, caused by a different proportion ofconcrete and polarization resistances, become hardly evident

120

140

160

180

200

220

240

0 0.15 0.3 0.45 0.6 0.75

pola

risat

ion

[mV]

x [m]

concrete resistivity 10 kΩm

constant potential constant current

potential sweep sheet resistance

igure 19.Calculated minimum polarization of each rebar for differentnode discretizations for a concrete resistivity of 10 kΩm

Fa

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in the anode/concrete interface for the given geometry. Theconsideration of the anode systems polarization resistivity viathe application of the potential sweep method leads to a moreuniform current distribution. The peaks presented by theconstant potential approach are flattened out especially for lowconcrete resistivities. This is caused by the proportions ofthe concrete and polarization resistances, resulting in theactivation of anode areas further away from the rebar positiondue to a total resistivity controlled current density distribution.This effect disappears for higher concrete resistivities. Further-more, it becomes obvious, that only the sheet resistanceapproach is accounting for the voltage drop within the anodematerial itself. This becomes apparent in the downward slopefrom the primary anode on the far left, to the right. The deviationfrom the mean anode current density is very high for the wetcase. In the vicinity of the primary anode, the calculated currentcorresponds to 218% of the mean value while the minimumcurrent density at the opposite side is only 58% for the testedprimary anode spacing. Analogous to the consideration of thepolarization resistivities, the effect of the sheet resistance onthe current distribution disappears for high concrete resistivitiesfor the tested anode material resistivity. However, this maychange for higher resistivities or thinner anode layers, caused,e.g., by wear or application failure.

Looking at the calculated anode potential distributions,given in Figs. 14–17, the findings made above are confirmed to agreat extent. It becomes evident, that the constant currentapproach is based on unrealistic assumptions. The uniformcurrent distribution discussed above pairs with a non-uniformpotential distribution which is not applicable for any anodematerial existent. The constant potential method now providesconstant potentials by definition.

The anode potentials of the potential sweep and the sheetresistance method lead to increasingly non-uniform potentialdistributions for higher concrete resistivities, caused by thehigher driving voltages needed due to the increasing ohmic dropwithin the concrete. Obviously the negligence of the anodematerials resistivity results in an erroneous assessment of theactual anode polarization, especially for the area near the primaryanode system.

Finally, the impact of the anode discretization on theeffective polarization of the rebar has to be discussed, as this is amajor field of application for the numerical simulation of CPfor RC structures. Figures 18 and 19 present the minimumpolarization on each rebar for the wet and dry case. It can be seen,that the constant current, constant potential, and potential sweepmethod show only little differences regarding the calculatedrebar polarizations for the wet case. The application of the sheetresistance approach results in a significant polarization increasefor the rebar near the primary anode and a decrease for thosefurther away. This is in good accordance with the observationsdiscussed above. Even though the 100mV criterion is fulfilledfor each rebar in the current case, the negligence of the anodematerials resistivity may lead to a harmful underestimation ofthe resulting rebar polarization for a wider spacing of the primaryanodes or different anode systems. For the dry case, the effect isless explicit. The higher polarizations calculated via the constantcurrent approach can be addressed to the unrealistic current



distribution at the anode surface. The point at the rebar surfaceexperiencing the minimum cathodic polarization is at the backfor the given geometric arrangement. The constant currentapproach forces the anode to deliver the mean protection currentin the middle of the rebar positions as well. From this point, thedifference of the resistances to the front and back of the rebar isless evident, see Fig. 4. However, this is very unlikely to be foundin a real structure.

7 Conclusions

In this paper, three different approaches for the discretizationof an ICCP anode system within a numerical model for theprediction of the current and potential distribution during theCP of RC structures have been compared to a novel approachproposed by the authors, the sheet resistance method. Allapproaches have been applied to a slab like geometry with asurface applied conductive coating CP anode system in order tocompare the different results.

The following conclusions have been found:

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The application of constant potentials or currents in order toreflect a CP anode system leads to non-realistic current andpotential distributions. However, constant potentials display arealistic current distribution for very high concrete resistivities.

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The consideration of the CP anodes polarization resistanceresults in a more homogeneous current density distributionfor reasonable concrete resistivities, while the effect disap-pears for very dry concrete.
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To assess a realistic current or potential distribution in theanode/concrete interface, e.g., to verify the compliance withcertain application boundaries, the sheet resistance of the CPanode has to be considered. This can be achieved by usage ofthe proposed sheet resistance method.
However, if themain purpose of themodeling procedure is arough estimation of the polarization of the reinforcement,simplified methods may also be applicable.

The calculations and the resulting conclusions are valid forsurface applied CP anode systems, especially for carbon-basedconductive coatings. The validity for discrete anode systems ordifferent anode materials, e.g., embedded MMOmesh has to bechecked via additional experiments and numerical studies.

Acknowledgements: The authors would like to thankGerman Research Foundation (DFG) and German Federationof Industrial Research Associations (AiF) for the funding of thisresearch.

8 References

[1] T. Eichler, B. Isecke, G. Wilsch, S. Goldschmidt, M. Bruns,presented at EUROCORR 2008, Edingburgh, Scotland, 7–11 September 2008, 15 pages.

2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

[2] T. Eichler, B. Isecke, G. Wilsch, S. Goldschmidt, M. Bruns,Mater. Corros. 2010, 61, 512.

[3] C. Helm, M. Raupach, C. Wolf, presented at EUROCORR2010, Moscow, Russia, 13–17 September 2010, 16 pages.

[4] C. Helm, T. Eichler, M. Raupach, B. Isecke, presented atEUROCORR 2011, Stockholm, Sweden, 4–8 September2011.

[5] DIN EN ISO 12696:2012–05, Cathodic protection of steel inconcrete (ISO 12696:2012); German version EN ISO12696:2012.

[6] J. E. Bennett, J. J. Bartholomew, J. Bushman, K. C. Clear,R. N. Kamp, W. J. Swiat, Cathodic Protection of ConcreteBridges: A Manual of Practice, National Reseach Council,Washington, DC 1993.

[7] M. Brem, Ph.D. Thesis, Numerische Modellierung derKorrosion in Stahlbetonbauten. Anwendung der BoundaryElement Methode, Eidgen€ossische Technische HochschuleZ€urich, Switzerland, 2004.

[8] J. Warkus, M. Raupach, Mater. Corr. 2010, 61, 494.[9] M. Raupach, M. Bruns, presented at 15th International

Corrosion Congress, Frontiers in Corrosion Science andTechnology, Granada, Spain, Septemper 22–27, 2002, Art.098, 8 pages.

[10] M. Raupach, presented at Technische Forschung und Beratungf€ur Zement und Beton, TFB. – Fachveranstaltung 824761/62,Betoninstandsetzung – aus Fehlern lernen, Wildegg, Switzerland,2003, chapter 5, 12 pages.

[11] J. Orlikowski, S. Cebulski, K. Darowicki, Cement ConcreteCompos. 2004, 16, 721.

[12] L. Bertolini, F. Bolzoni, T. Pastore, P. Pedeferri, CementConcrete Res. 2004, 34, 681.

[13] M. Bruns, M. Raupach, presented at EUROCORR 2004,Nice, France 12–16 September 2004, 10 pages.

[14] A. Asgharzadeh, M. Raupach, P. Henkel, D. Koch,presented at EUROCORR 2015, Graz, Austria, 6–10September 2015, 10 pages.

[15] A. Asgharzadeh, M. Raupach, D. Koch, presented atICCRRR 2015, Leipzig, Germany, 5–7 October 2015.

[16] A.A. Sag€ues, S.C. Kranc, B.G. Washington, presented atConcrete 2000, Dundee, Scotland, UK, 7–9 September 1993,pp. 1275–1284.

[17] A.M. Hassanein, G.K. Glass, N.R. Buenfeld, CementConcrete Compos. 2002, 24, 159.

[18] M. Raupach, J. Warkus, Mater. Corros. 2003, 54, 394.[19] M. Bruns, M. Raupach, presented at ICCRRR 2008,

Cape Town, South Africa, 24–26 November, 2008, pp. 301–302.

[20] M. Bruns, M. Raupach, presented at EUROCORR 2008,Edingburgh, Scotland, UK, 7–11 September 2008, 14 pages.

[21] M. Raupach, M. Bruns, presented atNACE 2008, Las Vegas,USA, October 6–10, 2008, 14 pages.

[22] C. Helm, M. Raupach, presented at Concrete Solutions 2014,Belfast, Northern Ireland, UK, 1–3 September 2014,pp.199–203.

(Received: January 6, 2016) W8832(Accepted: February 21, 2016)

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