Propagation of steel corrosion in concrete: Experimental and numerical investigations

Cement and Concrete Composites 70 (2016) 171e182

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Propagation of steel corrosion in concrete: Experimental and numerical investigations A. Michel a, *, M. Otieno b, H. Stang a, M.R. Geiker c a

Technical University of Denmark (DTU), Department of Civil Engineering, Kgs. Lyngby, Denmark University of the Witwatersrand, School of Civil and Environmental Engineering, Johannesburg, South Africa c Norwegian University of Science and Technology (NTNU), Department of Structural Engineering, Trondheim, Norway b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 January 2015 Received in revised form 5 June 2015 Accepted 9 April 2016 Available online 19 April 2016

This paper focuses on experimental and numerical investigations of the propagation phase of reinforcement corrosion to determine anodic and cathodic Tafel constants and exchange current densities, from corrosion current density and corrosion potential measurements. The experimental program included studies on RC specimens with various binder compositions, concrete cover thicknesses, and concrete cover crack widths. Modelling and fitting of experimental data using an electrochemical model allowed for the determination of parameters, which are key parameters for electrochemical modelling tools. The numerical model was, furthermore, used to identify electrochemical parameters, which are independent of concrete cover thickness and crack width and at the same time allow for determination of the corrosion current density and corrosion potential of concrete structures within an acceptable error. Very good comparisons between the experimentally measured and numerically simulated corrosion current densities and corrosion potentials were found for the various RC specimens. Anodic and cathodic Tafel constant between 0.01 and 0.369 V/dec and 0.01 and 0.233 V/dec, respectively, were found in the present study through numerical simulations of the experimental data. Anodic and cathodic exchange current densities ranged from 1.0Ee12 to 1.0Ee09 A/mm2 and 1.0Ee12 to 1.1Ee09 A/mm2, respectively. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Corrosion current density Cracked concrete Reinforcement Modelling Tafel value Exchange current density

1. Introduction Concrete is nowadays the most used manmade construction material in the world with an annual production of approximately 20 billion metric tons [1]. Low price and favourable engineering properties are main reasons for the success of concrete compared to other building materials, such as steel or timber. Concrete is often reinforced with steel, which helps to over-come shortcomings of both materials. Concrete has a high compressive strength, but a low tensile strength and is, therefore, reinforced for structural purposes, while the steel is protected by the concrete from potentially harming environmental exposure. Under certain circumstances, however, this “symbiosis” can be compromised resulting in deterioration of reinforced concrete (RC) structures, such as reinforcement corrosion. Corrosion of steel embedded in concrete is one of the major deterioration

* Corresponding author. E-mail address: [email protected] (A. Michel). URL: http://www.dtu.dk http://dx.doi.org/10.1016/j.cemconcomp.2016.04.007 0958-9465/© 2016 Elsevier Ltd. All rights reserved.

mechanisms in RC structures causing considerable losses to society due to maintenance and repair needs. In the United States alone, for example, it has been estimated that approximately $1.8 trillion (US) must be spent over the next 20 years to maintain the current state of roads and bridges. Moreover, $627 billion (US) [2] are required over that same time period to improve these infrastructure systems to adequate levels. The major part of degradation problems is thereby related to corrosion of reinforcing steel [3]. Corrosioninduced damages, such as concrete cracking, spalling, delamination, and cross sectional reduction of the reinforcement, may cause aesthetic damages, decrease the load bearing capacity of a structure, and in the worst-case lead to fatal structural consequences, such as failure. Within recent decades, the research community has placed much focus on studying the initiation, see e.g. Refs. [4e7] as well as propagation of corrosion processes in reinforced concrete structures, see e.g. Refs. [8e10]. In particular, with respect to the propagation of reinforcement corrosion a number of models and tools have been developed to describe corrosion processes in reinforced concrete structures, see e.g. Refs. [11e16]. The majority of the proposed models to describe the propagation of reinforcement

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corrosion require electrochemical input parameters, i.e. anodic and cathodic Tafel constants and exchange current densities, which have to be determined a priori. Consequently, at the same time a number of studies can be found in the literature, in which such electrochemical parameters were determined under defined laboratory conditions. Among others, it was found that the surface state of the electrode, temperature, moisture content, and geometry have a considerable influence on reinforcement corrosion processes, see e.g. Refs. [17,20e22]. For the anodic and cathodic Tafel constants a number of values have been published, which are mainly based on controlled labo
s et al. [23] investigated ratory experiments and data fitting. Garce corrosion of steel in neutral and acid solutions simulating electrolytic environments in concrete micropores during the propagation period and found anodic Tafel constants ranging from 0.073 to 0.136 V/dec and cathodic Tafel constants between 0.112 and 0.242 V/dec. Similar anodic (0.067e0.080 V/dec) and cathodic (0.222e0.239 V/dec) Tafel constants were found in Ref. [11] for steel in synthetic pore solutions and mortar subjected to temperatures varying between 5 and 47
C. Through theoretical analysis of the Stern-Geary equation [19], Song [24] found that the anodic Tafel constants may vary between 0.013 and 0.017 V/dec and the cathodic Tafel constants between 0.021 and 0.065 V/dec for active steel. Considerable higher values, i.e. anodic Tafel constants between 0.320 and 1.570 V/dec and cathodic Tafel constants between 0.380 and 1.080 V/dec, were found in Ref. [25] by means of galvanostatic polarisation tests of seven concretes with different percentages of sodium chloride. Chang et al. [26] found anodic and cathodic Tafel constants ranging from 0.077 to 0.089 V/dec and 0.449e1.215 V/dec, respectively, for steel bars embedded in concrete exposed to sea water. Similar to the anodic and cathodic Tafel constants, a wide range of values can be found in the literature for the anodic and cathodic exchange current density. Experimentally determined values for the anodic exchange current density range from 1.00Ee12 to 2.75Ee10 A/mm2, see e.g. Refs. [9,12,27e29]. For the cathodic exchange current density values between 6.00Ee12 and 10.00Ee12 €ggi [11] determined A/mm2 were proposed in e.g. Refs. [9,12,27]. Ja the anodic and cathodic exchange current density for steel in synthetic solutions and found values between 3.07Ee08 and 14.60Ee08 A/mm2 and 6.00Ee11 and 16.00Ee11 A/mm2, respectively. For steel in mortar conditioned to various relative humidities €ggi [11] found anodic exchange current denand temperatures, Ja sities ranging from 0.73Ee08 to 16.90Ee08 A/mm2 and cathodic exchange current densities between 1.00Ee12 and 8.50Ee10 A/ mm2. An overview of reported anodic and cathodic Tafel constants and exchange current densities is given in Table 1. The wide range of values for anodic and cathodic Tafel constants and exchange current densities published in the literature highlights the importance of these parameters in the analysis and (numerical) predictions of corrosion current density and corrosion potential in RC structures. Determination of electrochemical parameters is, however, often difficult or even impossible for in situ RC structures. This paper focuses on experimental and numerical investigations of the propagation phase of reinforcement corrosion. The experimental program included studies on RC specimens with various binder compositions, concrete cover thicknesses, and concrete cover crack widths. Numerical simulation and subsequent fitting of experimental data by means of an electrochemical model allowed for the determination of electrochemical parameters, i.e. anodic and cathodic Tafel constants and exchange current densities, which are key parameters for electrochemical modelling tools. The electrochemical model was also used to identify electrochemical parameters, which are independent of concrete cover thickness and crack width and at the same time allow for

Table 1 Overview of reported anodic and cathodic Tafel constants and exchange current densities. Parameter

Value

Unit

Reference

Anodic Tafel constant

0.073e0.136 0.067e0.080 0.013e0.017 0.320e1.570 0.077e0.089 0.112e0.242 0.222e0.239 0.021e0.065 0.380e1.080 0.449e1.215 1.00E-12e2.75E-10 3.07E-08e1.46E-07 0.73E-08e1.69E-07 6.00E-12e1.00E-11 6.00E-11e1.60E-10 1.00E-12e8.50E-10

V/dec V/dec V/dec V/dec V/dec V/dec V/dec V/dec V/dec V/dec A/mm2 A/mm2 A/mm2 A/mm2 A/mm2 A/mm2

[23] [11] [24] [25] [26] [23] [11] [24] [25] [26] [9,12] [11] [11] [9,12] [11] [11]

Cathodic Tafel constant

Anodic exchange current density

Cathodic exchange current density

determination of the corrosion current density and corrosion potential of concrete structures within an acceptable error. 2. Experimental investigations The experimental program of this study was designed to assess the influence of pre-corrosion flexural cover cracking on corrosion current density and corrosion potential. A total of 108 beams (120  130  375 mm3) were studied including five different concrete mix designs (with respect to binder type and w/b), two cover depths, and varying cover crack width. 2.1. Materials and specimen preparation Test specimens were cast with two w/b (0.40 and 0.55) and various combinations of Portland cement (PC) (CEM I 42.5N), ground granulated blast-furnace slag (GGBS), and fly ash (FA). The binder combinations were 100 PC, 50/50 PC/GGBS, and 70/30 PC/ FA, in mass percentage. For the 100 PC specimens, only specimens with a w/b of 0.4 were cast. An overview of concrete mix proportions and selected concrete properties is presented in Table 2. Other experimental variables included cover depth (20 and 40 mm) and crack width (0, 0.4, and 0.7 mm). High yield steel bars with a diameter of 10 mm and length of 370 mm were embedded in each beam. To facilitate the formation of transverse (flexural) cracking at approximately the longitudinal centre of the specimens during loading, a 1 mm thick and 4 mm deep PVC sheet was placed at the centre of each beam (transversely) during casting. The PVC sheet was embedded in the beam mould, and removed after de-moulding (after 24 h). Upon 28 days of water-curing (at 23 ± 2
C) and 10 days air-drying (25 ± 2
C and 50 ± 5% RH) in the laboratory, anodic impressed current was used to drive chlorides from the concrete surface (contained in a reservoir on the surface of the specimen, see Fig. 1) towards the reinforcement surface and initiate active corrosion in all specimens. An overview of the applied impressed currents can be found in Table 3. The impressed direct current was applied for 1.5 h, after which all specimens were connected in series and an effective direct current of 8.6 mA was applied for another 2 h. Application of 8.6 mA was expected to result in a corrosion current density of approximately 0.1 mA/cm2 in all specimens assuming that the complete steel surface area of 86 cm2 was polarized. A corrosion current density of 0.1 mA/cm2 was chosen in agreement with e.g. Refs. [30,31] to denote the transition from passive (initiation) to active (propagation) corrosion. Finally, the beams (except the uncracked ones) were pre-cracked under 3-

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Table 2 Overview of concrete mix proportions and selected properties. Binder composition

100 PC

50/50 PC/GGBS

w/b

0.40

0.40

0.55

0.40

0.55

3

Material [kg/m ]

Mix label

PC (CEM I 42.5N) GGBS FA Fine aggregate: Klipheuwel sand (2 mm max.) Coarse aggregate: Granite (13 mm max.) Water Superplasticizera (SP) Slump [mm] 28-day compressive strength [MPa] a b c d

70/30 PC/FA

PC-40

SL-40

SL-55

FA-40

FA-55

500 e e 529

231 231 e 749

168 168 e 855

324 e 139 749

236 e 101 855

960 200 2.1b (0.4)c 120 58.2 (3.0)d

1040 185 1.8 (0.4) 105 48.1 (2.0)

1040 185 0.3 (0.1) 150 35.3 (0.9)

1040 185 0.4 (0.1) 85 50.7 (0.9)

1040 185 e 200 28.6 (1.9)

Chemical base: Naphthalene Formaldehyde Sulphonate. Percentage of SP by mass of total binder. Amount of SP in L/m3. Standard deviation.

375 162.5

162.5 130 90

280

20

In-built salt solution reservoir

20 or 40

M14 nut and bolt

10 mm diam. reinforcing steel bar

20 or 40 30

10 mm diam. x 150 mm long stainless steel counter electrode

Beam cross-section

3 mm thick steel plates

120

20 mm diam. steel rod

Fig. 1. Customised cracking frames to maintain defined crack width at tensile surface (all dimensions in [mm]).

2.2. Corrosion potential, concrete resistivity, and corrosion current density measurements

Table 3 Overview of applied impressed current for various binder combinations. Binder composition

100 PC 50/50 PC/GGBS 50/50 PC/GGBS 70/30 PC/FA 70/30 PC/FA

Impressed current in [A] for cover thickness of w/b

Mix label

20 mm

40 mm

0.4 0.4 0.55 0.4 0.55

PC-40 SL-40 SL-55 FA-40 FA-55

0.03 0.44 0.25 0.57 0.44

0.13 1.67 1.01 1.70 1.67

point flexural machine loading. The pre-cracked specimens were then placed in specially designed loading rigs, see Fig. 1. Tightening of the bolts allowed for establishment of desired crack widths at the tensile surface, i.e. 0, 0.4, and 0.7 mm, which was measured with a demountable mechanical strain gauge (DEMEC). The test specimens were placed for the entire duration of the study in the loading rigs to reduce closing of the cracks. After cracking, specimens were subjected to cyclic wetting (3 days) with 5% NaCl solution (contained in a reservoir on the tensile face of the beam, see Fig. 1) followed by 4 days air-drying to accelerate corrosion for a period of approximately 120 weeks.

Corrosion current density, corrosion potential, and concrete resistivity (by means of 4-point Wenner probe) were measured twice a week for a period of approximately 120 weeks. Corrosion potentials by means of half-cell potential (HCP) measurements were conducted against a silver/silver chloride electrode (Ag/AgCl). The reference electrodes were maintained on a weekly basis. Maintenance included refilling with saturated potassium chloride solution, potassium chloride crystals, and calibration against a saturated calomel reference electrode in a pH buffered solution. Due to the frequent maintenance and constant temperature of the exposure solution, the readings of the reference electrode were stable. For the concrete resistivity measurements, the Wenner probe apparatus was placed a distance away from the steel during the measurements to avoid any influence of the reinforcement steel i.e. no resistivity measurements were taken directly above the embedded steel bar. Furthermore, no surface wetting was required prior to resistivity measurements as it was carried out at the end of the 3-day wetting period. Corrosion current densities were obtained by means of the coulostatic technique, which is a linear polarisation resistance method, where a small charge is applied to the steel and the relaxation of the corrosion potential is monitored

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3

2.5

Corrosion current density [μA/cm2]

Corrosion current density [μA/cm2]

0.6 PC−40 (CEM 1 42.5N) w/b 0.40 40 mm cover depth

2

1.5

1

0.5

0 0

Uncracked 0.4 mm cracked 0.7 mm cracked 20

40

60 80 Time [weeks]

100

0.4 0.3 0.2

0 0

120

0.9

SL−55 w/b 0.55 40 mm cover depth

0.6 0.4 0.2

Uncracked 0.4 mm cracked 0.7 mm cracked 20

40

60 80 Time [weeks]

100

120

Corrosion current density [μA/cm2]

Corrosion current density [μA/cm2]

20

40

60 80 Time [weeks]

100

120

1

0.8

0 0

Uncracked 0.4 mm cracked 0.7 mm cracked

0.1

1.2 1

SL−40 w/b 0.40 40 mm cover depth

0.5

0.8 0.7

FA−40 w/b 0.40 40 mm cover depth

0.6 0.5 0.4 0.3 0.2

Uncracked 0.4 mm cracked 0.7 mm cracked

0.1 0 0

20

40

60 80 Time [weeks]

100

120

Corrosion current density [μA/cm2]

1.5

FA−55 w/b 0.55 40 mm cover depth 1

0.5

0 0

Uncracked 0.4 mm cracked 0.7 mm cracked 20

40

60 80 Time [weeks]

100

120

Fig. 2. 2-point moving average corrosion current density for test specimens with a cover depth of 40 mm, various binder combinations, and crack widths at tensile surface. (Please note: varying ordinate scale).

over a short period of time to determine the polarisation resistance, RP, [32,33]. RP is related to the corrosion current, Icorr, by means of the Stern-Geary coefficient B, i.e. Icorr ¼ B/Rp. The Stern-Geary coefficient may vary between 13 and 52 mV depending on the corrosion state of the steel (i.e. passive or active). A value of 26 mV for corroding (active) steel and of 52 mV for passive steel in the case of concrete has been established and used by a number of

researchers; see e.g. Refs. [34e36]. In this study, therefore, a value of 26 mV was used. The corrosion current density was subsequently obtained dividing Icorr by the complete steel surface area, i.e. 86 cm2. However, it must be acknowledged that this assumption may lead to under-estimation of the actual corrosion current density and consequently the predicted penetration depth; in particular, for cracked RC where local pitting may occur in the vicinity of

Corrosion current density [μA/cm2]

3 2.5

PC−40 (CEM 1 42.5N) w/b 0.40 20 mm cover depth

2 1.5 1 Uncracked 0.4 mm cracked 0.7 mm cracked

0.5 0 0

20

40

60 80 Time [weeks]

100

Corrosion current density [μA/cm2]

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175

SL−40 w/b 0.40 20 mm cover depth

1

0.8

0.6

0.4

0.2

Uncracked 0.4 mm cracked 0.7 mm cracked

0 0

120

20

40

60 80 Time [weeks]

100

120

1.6

Corrosion current density [μA/cm2]

1.2

SL−55 w/b 0.55 20 mm cover depth

1 0.8 0.6 0.4 Uncracked 0.4 mm cracked 0.7 mm cracked

0.2 20

40

60 80 Time [weeks]

Corrosion current density [μA/cm2]

0 0

2

100

120

Corrosion current density [μA/cm2]

1.2 1.4

1

FA−40 w/b 0.40 20 mm cover depth

0.8 0.6 0.4 Uncracked 0.4 mm cracked 0.7 mm cracked

0.2 0 0

20

40

60 80 Time [weeks]

100

120

FA−55 w/b 0.55 20 mm cover depth

1.5

1

0.5

0 0

Uncracked 0.4 mm cracked 0.7 mm cracked 20

40

60 80 Time [weeks]

100

120

Fig. 3. 2-point moving average corrosion current density for test specimens with a cover depth of 20 mm, various binder combinations, and crack widths at tensile surface. (Please note: varying ordinate scale).

the cracked region. To account for local pitting corrosion, pitting factors can be introduced, see e.g. Ref. [37]. Therefore, within the present study, average values of the latest measurements (i.e. after around 94 weeks of exposure) were used to fit experimental data by means of the electrochemical model assuming that the complete steel surface is corroding.

2.3. Experimental results Experimentally determined corrosion current densities for the various binder combinations, w/b, cover depths, and crack widths are presented in Figs. 2 and 3. Average corrosion current densities and corrosion potentials, determined from data collected between

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Table 4 Experimentally measured corrosion current density (icorr) and corrosion potential for different concrete mix designs and surface crack widths. Mix label

Resistivitya [kU cm]

Cover [mm]

Crack width [mm] 0.0

0.4

0.7

icorr [mA/cm ] a

PC-40

30

SL-40

84

SL-55

68

FA-40

93

FA-55

44

a b

20 40 20 40 20 40 20 40 20 40

1.69 1.50 0.43 0.35 0.63 0.55 0.52 0.46 1.11 0.64

2

0.0

0.4

Corrosion potential 2.09 1.92 0.66 0.45 0.82 0.75 0.82 0.63 1.56 0.91

2.91 2.74 1.00 0.53 1.41 1.03 1.05 0.75 2.09 1.20

633 547 444 413 469 421 471 427 500 485

a,b

688 593 483 449 513 481 499 469 554 554

0.7 [-mV] 568 482 331 324 400 377 369 348 430 380

Average weeks 94e100. Corrosion potential measured against Ag/AgCl electrode.

Fig. 4. Overview of electrochemical and physical processes describing corrosion of steel in concrete, from Ref. [39].

weeks 94 and 100, are presented in Table 4. In general, an increasing corrosion current density over time is observed for all specimens within the approximately first 90 weeks. The measured increase in corrosion current density was independent of cover depth, crack width, and concrete quality, i.e. binder composition and w/b. More steady corrosion current densities were observed after that and the effect of cover depth, crack width, and concrete quality (binder type and w/b ratio) on the corrosion current density can be seen from the presented results. From the results presented it can be generally stated that the: (i) corrosion current density is affected by the crack width, increasing corrosion current densities were measured for specimens (independent of cover thickness and concrete quality) with increasing crack width. (ii) corrosion current density is affected by the cover depth, higher corrosion current densities were experimentally determined for specimens with lower cover thickness independent of binder combination and w/b. (iii) concrete quality affects corrosion current densities, increasing corrosion current densities were measured for decreasing concrete quality, i.e. with respect to binder combination and w/b. Similar trends, as seen for the corrosion current density, were observed for the experimentally measured corrosion potentials. Overall, high corrosion current densities corresponded to more

negative corrosion potentials. A holistic view of the results showed that, in general, corrosion current densities increased with increasing crack width but the extent of the increase was dependent on both concrete quality and cover depth. 3. Numerical investigations 3.1. Modelling approach Corrosion of steel in concrete can be described by the same electrochemical processes as the corrosion of a metal in an electrolyte [38]. Fig. 4 gives an overview of electrochemical and physical processes describing the corrosion of steel in concrete, which was proposed by Küter in Ref. [39]. Two electrochemical half-cell reactions must take place at the metal surface, the anodic (oxidation) and the cathodic (reduction) half-cell reactions, for corrosion to occur. The anodic half-cell reaction is thereby always characterised by liberating electrons, which are consumed in the cathodic half-cell reaction. To avoid local accumulation of electrical charges, the liberated electrons are conducted through the metal to the cathode establishing an electrical connection between the anode and cathode. The electrical circuit is then closed by an ionic exchange current through the electrolyte. Typically, the oxidation of iron is assumed as anodic half-cell reaction, which can be given as follows:

Fe/Fe2þ þ 2e

(1)

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At the cathode the reduction of oxygen is commonly assumed, which can be given as follows:

1 O þ H2 O þ 2e /2OH 2 2

(2)

However, depending on the potential and pH at the steel surface, other cathodic reactions, such as the reduction of water, may take place. A detailed overview of thermodynamically feasible anodic and cathodic reactions associated with reinforcement corrosion can be found in e.g. Ref. [39]. In principle, two equations can be used to describe the electrochemical processes in the concrete pore solution acting as electrolyte, see e.g. Refs. [12,16,27]. The first one is Laplace's equation, which describes the potential distribution in the electrolyte assuming electrical charge conservation and isotropic conductivity:

V2 E ¼ 0

177

Table 5 Model parameters used to fit experimentally measured corrosion current density and corrosion potential for different concrete mix designs and surface crack widths. Parameter

Symbol

Value Lower

Anode length Anode diameter Cathode length Cathode diameter Cover thickness Concrete resistivity Temperature Limiting corrosion current density Anodic exchange current density Cathodic exchange current density Anodic equilibrium potential Cathodic equilibrium potential Anodic Tafel constant Cathodic Tafel constant

la da lc dc c

U T ilim i0a i0c E0a E0c ba bc

0.275 0.01 0.15 0.01 0.02 See Table 298.15 1E-6 1Ee12 1Ee12 0.540 0.405 0.02 0.01

Unit Upper

0.04 3

7Ee9 7Ee9

0.4 0.25

m m m m m kU cm K A/mm2 A/mm2 A/mm2 VSHE VSHE V/dec V/dec

(3)

The second is Ohm's law, which can be used to determine the rate of dissolution of iron at any point on the steel surface in concrete if the potential distribution around that point and the resistivity of the electrolyte is known, see e.g. Refs. [10,27]:

1

vE

(4)

rconc vn

where rconc is the concrete resistivity and n the direction normal to the rebar surface. Once corrosion is initiated, the potentials of the half-cell reactions on the steel surface are shifted from their equilibrium potentials, E0, and a (corrosion) current will start to flow. The shift from the equilibrium potential is known as polarisation and the kinetics of the electrochemical half-cell reactions are governed by the degree of polarisation. A measure for the polarisation is the overpotential, h, which is the difference between the corrosion potential, E, and the equilibrium potential of the anode and cathode, E0a/0c, respectively. Depending on the mechanism, four types of polarisation acting individually or in combination may be distinguished; namely, activation, concentration, resistance, and crystallisation polarisation, see e.g. Ref. [17]. In the present work, crystallisation polarisation is neglected, and only the effects of activation, concentration, and resistance polarisation are taken into account, see e.g. Ref. [18].

−0.6

(a)

potcorr 2D

Corrosion potential [VSCE]

potcorr 3D

−0.65

−0.7

−0.75 0

0.05

0.1 0.15 0.2 Rebar length [m]

0.25

icorr;a=c ¼ i0 expðJÞ

with J ¼ lnð10Þ

E  E0 b

(5)

where icorr,a/c is the corrosion current density of anode and cathode, respectively, i0, the exchange current density, E the corrosion potential, E0 the equilibrium potential, and b the Tafel constant, which is defined as follows:

b ¼ lnð10Þ

RT

(6)

azF

where R is the universal gas constant, T the absolute temperature, a the charge transfer coefficient, z the valence, and F Faraday's constant. To include the effects of concentration polarisation on the relation between the corrosion potential and the corrosion current density, Equation (5) can be extended and written as follows, see e.g. Ref. [20]:

2 Corrosion current density [μA/cm2]

icorr ¼ 

For activation polarisation, the relation between the corrosion current density and the corrosion potential may be described by the Butler-Volmer equation as follows (assuming that the electrochemical reactions take place at separate electrodes and the polarisation is high), see e.g. Ref. [19]:

(b)

icorr 2D icorr 3D

1.5

1

0.5

0 0

0.05

0.1 0.15 0.2 Rebar length [m]

0.25

Fig. 5. Comparison between numerical results, (a) corrosion potential and (b) corrosion current density, representing experimental geometry by 2D and 3D model.

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Fig. 6. Comparison of experimental (flat surface) and numerical results of (a) corrosion current density and (b) corrosion potential for different combinations of ba and bc for uncracked specimen with 40 mm concrete cover (see PC-40 in Table 4).

the overpotential at the anode and cathode, see e.g. Refs. [17e20]. Therefore, a great variety of Tafel values, (equilibrium potentials), and exchange current densities for the anodic and cathodic half-cell reaction governing the polarisation curves can be found in the literature. The equilibrium potentials for the anodic and cathodic half-cell reaction can be calculated from the Nernst equation:

0.25

bc [V/dec]

0.2

0.15

0.1

E0 ¼ E00 

0.05 Corrosion current density Corrosion potential

0 0

0.05

0.1

0.15 ba [V/dec]

0.2

0.25

Fig. 7. Combination of parameters ba and bc that fit either experimentally measured corrosion current density (circle markers) or corrosion potential (square markers) for uncracked specimen with 40 mm concrete cover (see PC-40 in Table 4).

 icorr;a=c ¼ i0 exp

 1J 1 þ i0 =ilim J

(7)

where ilim is the limiting corrosion current density, which can be defined as follows, see e.g. Ref. [18]:

ilim ¼

zFDO2

d

CO2

(8)

where DO2 is the oxygen diffusion coefficient, CO2 the oxygen concentration at the electrode surface and d the diffusion layer thickness. A number of factors influence the shape of polarisation curves, which in turn govern the kinetics of the corrosion process. Among others, the surface condition of the electrode (e.g. surface roughness), temperature, moisture content, and geometry are decisive for

  lnð10ÞRT aox log zF ared

(9)

where E00 is the standard potential, aox the chemical activity of the oxidant, and ared the chemical activity of the reductant. Assuming Equations (1) and (2) are the governing half-cell reactions, the equilibrium potentials for the anodic and cathodic half-cell reaction can be calculated as function of the chemical activity and temperature. For the anodic half-cell reaction, equilibrium potentials between 0.667 and 0.475 VSHE are obtained for chemical activities of the oxidant of 1 (common assumption for solid matter) and values ranging from 1E-06 to 1 for the reductant, respectively. No significant influence of temperature between 273.15 and 323.15 K is observed. For chemical activities of the reductant between 1E-03 and 1E-02, which can be expected in concrete, anodic equilibrium potentials between 0.534 and 0.562 VSHE are obtained. The determined anodic equilibrium potentials are thereby in good agreement with values reported in the literature, see e.g. Refs. [9,12,29]. Thus, for numerical simulations an anodic equilibrium potential of 0.540 VSHE was chosen. Cathodic equilibrium potentials between 0.401 and 1.302 VSHE are obtained for the same temperature range with a strong dependence on pH values between 0 and 14. However, for pH values between 13 and 14, which can be expected in non-carbonated concrete, cathodic equilibrium potentials vary between 0.405 and 0.463 VSHE with negligible influence of temperature. Similar values have been proposed in e.g. Refs. [9,12,29]. Thus, for numerical simulations a cathodic equilibrium potential of 0.405 VSHE was chosen.

A. Michel et al. / Cement and Concrete Composites 70 (2016) 171e182

(a)

(b) 3 2.5 2 1.5

increasing crack width

1 0.5 0

(c)

0 Corrosion potential [VAg/AgCl]

PC−40 SL−40 SL−55 FA−40 FA−55

PC−40 SL−40 SL−55 FA−40 FA−55

−0.2 −0.4 −0.6 −0.8 −1

Binder composition [−]

Binder composition [−]

(d) 3.5

PC−40 SL−40 SL−55 FA−40 FA−55

3 2.5 2 1.5

increasing crack width

1 0.5 0

Binder composition [−]

0 Corrosion potential [VAg/AgCl]

Corrosion current density [μA/cm2]

3.5

Corrosion current density [μA/cm2]

179

PC−40 SL−40 SL−55 FA−40 FA−55

−0.2 −0.4 −0.6 −0.8 −1

Binder composition [−]

Fig. 8. Comparison between numerical (hollow markers) and experimentally (solid markers) measured corrosion current density ((a) and (c)) and corrosion potential ((b) and (d)) for investigated mix designs and cover thickness ((a) and (b): 20 mm, (c) and (d): 40 mm), and surface crack widths (see Table 4 for experimental data).

3.2. Determination of electrochemical parameters To simulate and fit experimental results (see Table 4), the commercial finite element method (FEM) software package Comsol Multiphysics was used. To save computational time the 3D problem was represented by a 2D geometry. Preliminary simulations showed that corrosion current densities as well as corrosion potential distribution within the domains are comparable for both geometries. By way of an example, results of the comparison are presented in Fig. 5, for the average corrosion current density and corrosion potential along the anode. The 2D geometry consisted of 17,700 triangular elements with quadratic shape functions and 8950 nodes representing the concrete and steel domain. Corrosion potential distribution was computed within the concrete and steel domain and the corrosion current density was determined at the concrete-steel interface. Neumann boundary conditions, i.e. vE/ vn ¼ rconcicorr,a/c (see also Equation (5)), were defined at the concrete-steel interface, while zero flux boundary conditions, i.e. vE/vn ¼ 0, were defined for the remaining boundaries. A finer mesh was created along the reinforcement to ease convergence due to the high non-linearity imposed by the physical problem. For the solution of the steady-state problem a linear direct solver (LU factorization) was used. The accuracy of the solution was controlled through an appropriate error check, which asserted that the product of the relative error and stability constant was sufficiently

small. Input parameters to simulate the experimental data are given in Table 5. Anodic and cathodic Tafel constants and exchange current densities were varied within the ranges documented in the literature during the numerical simulations. This resulted in 4900 simulations for each concrete mix and cover thickness (see Table 2), i.e. a total of 49,000 simulations. To find the parameter combination simulating the experimental data, numerically determined corrosion current density and corrosion potential for all parameter combinations were compared to the experimentally measured data, for each concrete mix, cover thickness, and crack width (see Table 4). The principle of the data fitting is illustrated in Fig. 6 (a) and (b) for variations of the anodic and cathodic Tafel constants. Results of the numerical simulations (surface plot) are plotted together with the experimental data (flat surface) for the corrosion current density and corrosion potential. As can be seen from the plots, a variety of parameter combinations can be found from Fig. 6 (a) and (b), which fit either the experimentally measured corrosion current density or corrosion potential. Parameter combinations of anodic and cathodic Tafel constants which fit either the experimentally measured corrosion current density (circle markers) or corrosion potential (square markers) are illustrated in Fig. 7. To fit experimentally obtained corrosion current density and corrosion potential at the same time, a limited set of parameter combinations is found, i.e. the intersection between both curves. The principle

180

A. Michel et al. / Cement and Concrete Composites 70 (2016) 171e182

Table 6 Model parameters providing best fit of experimentally measured corrosion current density and corrosion potential (see Table 4 and Fig. 8). Mix label []

w/b []

Cover [mm]

Crack width [mm]

ba [V/dec]

bc [V/dec]

i0a [A/mm2]

i0c [A/mm2]

PC-40 SL-40 SL-55 FA-40 FA-55 PC-40 SL-40 SL-55 FA-40 FA-55 PC-40 SL-40 SL-55 FA-40 FA-55 PC-40 SL-40 SL-55 FA-40 FA-55 PC-40 SL-40 SL-55 FA-40 FA-55 PC-40 SL-40 SL-55 FA-40 FA-55

0.40 0.40 0.55 0.40 0.55 0.40 0.40 0.55 0.40 0.55 0.40 0.40 0.55 0.40 0.55 0.40 0.40 0.55 0.40 0.55 0.40 0.40 0.55 0.40 0.55 0.40 0.40 0.55 0.40 0.55

40

0.0

40

0.4

40

0.7

20

0.0

20

0.40

20

0.70

0.044 0.080 0.073 0.073 0.052 0.082 0.066 0.076 0.133 0.045 0.088 0.101 0.079 0.090 0.077 0.076 0.069 0.058 0.060 0.045 0.022 0.054 0.274 0.048 0.206 0.093 0.369 0.010 0.300 0.195

0.064 0.077 0.050 0.060 0.088 0.123 0.055 0.035 0.065 0.062 0.053 0.099 0.102 0.107 0.076 0.160 0.233 0.064 0.095 0.038 0.010 0.044 0.124 0.101 0.092 0.072 0.088 0.010 0.010 0.035

1.2Ee11 1.0Ee12 1.0Ee12 1.0Ee12 1.0Ee12 1.1Ee09 1.0Ee12 1.2Ee11 1.0Ee09 1.2Ee11 1.0Ee10 1.0Ee12 1.0Ee12 1.0Ee12 1.0Ee12 3.3Ee09 1.0Ee12 1.0Ee12 1.0Ee12 1.0Ee12 6.7Ee09 1.0Ee12 1.1Ee09 1.0Ee12 2.2Ee09 1.2Ee09 6.3Ee10 7.6Ee10 5.6Ee10 6.3Ee10

3.4Ee11 1.0Ee12 1.0Ee12 4.5Ee11 1.0Ee12 6.6Ee09 1.0Ee12 2.3Ee11 5.6Ee09 1.0Ee12 4.5Ee09 1.0Ee12 3.3Ee09 3.3Ee09 1.0Ee12 1.1Ee09 1.1Ee09 2.3Ee11 1.1Ee09 2.3Ee11 6.7Ee09 6.7Ee09 1.0Ee12 3.3Ee09 1.0Ee12 2.3Ee09 3.0Ee09 3.3Ee09 3.0Ee09 3.0Ee09

can be extended to multiple parameter adaptation; however, due to the complex nature of visualisation of the procedure, fitting of only two parameters was given here by way of example. 4. Comparison between experimental and numerical results Comparisons between experimentally measured and numerically simulated corrosion current densities and corrosion potentials are presented in Fig. 8. As can be seen from the results, very good agreements between the experimental data and numerical simulation can be found for the various concrete mixes, cover thicknesses, and crack widths. Through variation of the anodic and cathodic Tafel constants and exchange current densities, the electrochemical model is able to simulate experimentally determined corrosion current density and corrosion potential. Parameter combinations providing the best fit of the experimental data are given in Table 6. Anodic and cathodic Tafel constant between 0.01 and 0.369 V/dec and 0.01 and 0.233 V/dec, respectively, were found in the present study through numerical simulations of the experimental data. No clear trend with respect to binder composition, cover thickness, or crack width was observed for the numerically determined cathodic and anodic Tafel constants. Anodic and cathodic exchange current densities ranged from 1.0Ee12 to 1.0Ee09 A/mm2 and 1.0Ee12 to 1.1Ee09 A/mm2, respectively. Similar to the Tafel constants, no dependencies on binder composition, cover thickness, or crack width was observed. 5. Discussion As outlined in the introduction, numerical simulation of reinforcement corrosion for the service life prediction of RC structures is becoming more common. In many cases electrochemical input parameters (which have to be determined a priori) are required for these models to describe and predict the reinforcement corrosion

process. Determination of these electrochemical parameters is, however, often difficult or even impossible for in situ structures. In the present study, experimental data of RC specimens with varying binder compositions, concrete cover thicknesses, and concrete cover crack widths were used to determine anodic and cathodic Tafel constants and exchange current densities. In the following sections the results obtained in the present study by the experimental and numerical techniques outlined previously are discussed. It should be noted that the present study focused on the determination of electrochemical modelling parameters by fitting of experimental data. Factors such as surface state of the electrode, moisture content, etc. which are known to influence the anodic and cathodic Tafel constants and exchange current densities were not taken into account in the present study. Comparisons between experimental data and numerical results (see Fig. 8) clearly illustrated the capability of the electrochemical model to simulate reinforcement corrosion processes for RC specimens with varying binder composition, cover thickness, and crack width. The electrochemical modelling parameters were determined by fitting of experimental data and chosen within the range previously reported in the literature. The considerable variation over several orders of magnitude for Tafel constants and exchange current densities (see Table 6) illustrate the importance of correct input parameters, in particular electrochemical parameters, of numerical tools to make realistic assessments and predictions of corrosion current density and corrosion potential in RC structures. As mentioned previously, in situ determination of Tafel constants and exchange current densities is often associated with problems and destructive investigations. It is, therefore, of interest to find electrochemical parameters (avoiding in situ determination), which can be used in electrochemical modelling tools for the assessment and prediction of corrosion current density and corrosion potential in RC structures. In this study, the previously presented electrochemical model was used to find sets of

A. Michel et al. / Cement and Concrete Composites 70 (2016) 171e182

2.5 2 increasing crack width

1.5 1 0.5 0

Corrosion current density [μA/cm2]

3.5

0

PC−40 SL−40 SL−55 FA−40 FA−55

3 2.5 2 increasing crack width

1.5 1 0.5 0

−0.2 −0.4 −0.6 −0.8 −1

Binder composition [−]

(c)

0

Binder composition [−]

(d)

PC−40 SL−40 SL−55 FA−40 FA−55

−0.2 −0.4 −0.6 −0.8 −1

Binder composition [−]

PC−40 SL−40 SL−55 FA−40 FA−55

(b) Corrosion potential [VAg/AgCl]

3

PC−40 SL−40 SL−55 FA−40 FA−55

(a)

Corrosion potential [VAg/AgCl]

Corrosion current density [μA/cm2]

3.5

181

Binder composition [−]

Fig. 9. Numerical (hollow markers) and experimentally (solid markers) measured corrosion current density and corrosion potential within a 30% deviation (error bar) from numerical simulation for investigated binder compositions, cover thickness ((a) and (b): 20 mm, (c) and (d): 40 mm), and crack width (see also Table 4 for experimental data).

Table 7 Model parameters to fit experimentally measured corrosion current density and corrosion potential for different concrete mix designs and surface crack widths (see also Table 4 and Fig. 8). Mix label []

w/b []

Cover [mm]

Crack width [mm]

ba [V/dec]

bc [V/dec]

i0a [A/mm2]

i0c [A/mm2]

PC-40 SL-40 SL-55 FA-40 FA-55 PC-40 SL-40 SL-55 FA-40 FA-55

0.40 0.40 0.55 0.40 0.55 0.40 0.40 0.55 0.40 0.55

20

0.0 0.4 0.7

40

0.0 0.4 0.7

0.180 0.200 0.300 0.120 0.320 0.150 0.121 0.138 0.104 0.075

0.098 0.023 0.010 0.023 0.023 0.068 0.118 0.081 0.049 0.150

7.0Ee09 7.4Ee10 1.1Ee09 7.4Ee10 1.8Ee09 1.5Ee09 1.1Ee10 2.1Ee10 1.1Ee10 1.1Ee10

1.5Ee09 1.1Ee09 1.0Ee12 6.3Ee09 6.6Ee09 3.3Ee09 7.4Ee10 3.7Ee09 3.7Ee09 1.1Ee09

electrochemical parameters, which are independent of binder composition, cover thickness, and crack width. To find such electrochemical parameters, the same principle as described before (see Section 3.2) was used. Results of these investigations are presented in Fig. 9 for the investigated concrete mixes, cover thicknesses, and crack widths. As can be seen from the results, predictions of corrosion current density and corrosion potential can be obtained within a 30% deviation for individual binder compositions independent of crack width. A considerable higher deviation is found (approximately 80%) predicting corrosion current density and corrosion potential for individual binder compositions independent of crack width and cover thickness. The parameter

combinations, which were found for the investigated binder compositions, are presented in Table 7. No correlation between electrochemical parameters and cover thickness was observed in this study. The lacking correlation indicates that other factors, such as surface state of the electrode, moisture content, temperature, etc. should be incorporated in analyses for an accurate determination of corrosion processes in RC. 6. Conclusions In this study, experimental data of RC specimens with varying binder compositions, cover thickness, and crack widths were used

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to demonstrate the applicability of an electrochemical modelling tool for reinforcement corrosion. Modelling and fitting of experimental investigations allowed for the determination of electrochemical parameters, i.e. anodic and cathodic Tafel constants and exchange current densities, which are key parameters for electrochemical modelling tools. Results presented in this study have clearly demonstrated the capability of the electrochemical model to simulate reinforcement corrosion processes in concrete specimens with varying binder composition, cover thickness, and crack width. Electrochemical parameters found in this study were within the range presented previously in the literature. Anodic and cathodic Tafel constant between 0.01 and 0.369 V/dec and 0.01 and 0.233 V/dec, respectively, were found in the present study through numerical simulations of the experimental data. Anodic and cathodic exchange current densities ranged from 1.0Ee12 to 1.0Ee09 A/mm2 and 1.0Ee12 to 1.1Ee09 A/mm2, respectively. The considerable variation over several orders of magnitude for Tafel constants and exchange current densities illustrate the importance of correct input parameters of numerical tools to make realistic assessments and predictions of corrosion current density and corrosion potential in RC structures. The results, furthermore, indicate that factors, such as surface state of the electrode, moisture content, temperature, etc. are decisive for realistic assessment and prediction of corrosion processes in RC. The electrochemical model could be further used to determine electrochemical parameters that allow for predictions within a 30% deviation from experimental data for individual binder compositions independent of crack width. Predictions of corrosion current density and corrosion potential for individual binder compositions independent of cover thickness and crack width were accompanied with considerable higher deviations (approximately 80%) from the experimental data. Acknowledgements The first author gratefully acknowledges the financial support of Otto Mønsteds Fond as well as Danish Expert Centre for Infrastructure Constructions for facilitating the research behind this paper. The second author acknowledges with gratitude the financial support received from: The University of Cape Town, the erstwhile Cement and Concrete Institute (C&CI), The National Research Foundation (NRF), Sika (SA) Pty Ltd., PPC Ltd, AfriSam, The Tertiary Education Support Programme (TESP) of ESKOM, and the South African Water Research Commission (WRC). References [1] L.R. Brown, Eco-Economy: Building an Economy for the Earth, Earth Policy Institute, W.W. Norton & Co, New York, 2001. [2] American Association of State Highway and Transportation Officials, The Bottom Line, AASHTO, Washington, D.C., USA, 2002, pp. 1e5. [3] F. Rendell, R. Jauberthie, M. Grantham, Deteriorated Concrete e Inspection and Physicochemical Analysis, first ed., Thomas Telford, London, UK, 2002. [4] E.J. Hansen, V.E. Saouma, Numerical simulation of reinforced concrete deterioration e part I: chloride diffusion, ACI Mater. J. 96 (1996) 173e180. [5] L. Marsavina, K. Audenaert, G. De Schutter, N. Faur, D. Marsavina, Experimental and numerical determination of the chloride penetration in cracked concrete, Constr. Build. Mater. 23 (1) (2009) 264e274. [6] P.F. Marques, A. Costa, Service life of RC structures: carbonation induced corrosion. Prescriptive vs. performance-based methodologies, Constr. Build. Mater. 24 (3) (2010) 258e265.
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