Concrete Repair,Rehabilitation and Protection

Proceedings of the International Conferenceheld at the University of Dundee, Scotland, UKon 27-28 June 1996

Edited by .

Ravindra K. DhirDirector, Concrete Technology UnitUniversity of Dundee

and

M. Roderick JonesLecturer, Concrete Technology UnitUniversity of Dundee

MATHEMATICAL MODELLING OF CHLORIDEEFFECT ON CONCRETE DURABILITY

AND PROTECTION MEASURES

V G Papadakis

A P Roumeliotis

M N Fardis

C G Vagenas

University ofPatras

Greece

ABSTRACT. In marine and coastal environments, or in the presence of deicing salts,penetration of chloride ions is one of the main mechanisms causing concretereinforcement corrosion. In this paper, a mathematical model of the physicochemicalprocesses of chloride penetration/binding in concrete is presented. This model allowsestimation of the time required for the chloride concentration surrounding thereinforcement to increase over the threshold of depassivation of reinforcing bars.Typical values of the physicochemical parameters of the model, such as kinetic constantsand diffusivity, are presented and related to concrete composition parameters. On thebasis of parametric analyses, protection measures against chloride-induced depassivationof steel in concrete are proposed.

Dr Vagelis G. Papadakis is a postdoctoral researcher in the Institute of ChemicalEngineering and High Temperature Chemical Processes and in the Chern. Eng. Dept.of the University of Patras, Greece. His main research interest is in the mathematicalmodeling and the experimental investigation of problems related to concrete durability.

Mr Alexis P. Roumeliotis is a graduate student in Chemical Engineering at theUniversity of Patras, specializing in numerical analysis and in the use of computers inchemical reaction engineering.

Professor Michael N. Fardis is a Professor of Concrete Structures and Director of theStructures Laboratory in the Civil Eng. Dep. of the Univ. of Patras. He has authoredmany papers on behaviour and modeling of concrete and concrete structures.

Professor Constantin os G. Vagenas is Professor of Reaction Engineering and Cataly-sis in the Chern. Eng. Dept. of the University of Patras. He has authored many papersin catalysis, high-temperature Electrochemistry and modeling of chemical processes.

Concrete Repair, Rehabilitation and Protection. Edited by R K Dhir and M R Jones. Publishedin 1996 by E & FN Spon, 2-6 BOlll1daryRow, London SE 1 8H:N, UK. ISBN 0 419 21490 9.

Corrosion of reinforcing bars is recognised today to be the single most limiting factorof the service life of reinforced concrete structures. It impairs not only the appearanceof the structure due to staining and spalling of the concrete cover, but also its strengthand safety, due to the reduction in the cross-sectional area of the reinforcement and tothe deterioration of bond with the surrounding concrete. Steel bars are passive, as faras corrosion in the presence of oxygen and moisture is concerned, thanks to amicroscopically thin oxide layer which forms on their surface due to the alkalinity of thesurrounding concrete. This protective layer is dissolved if alkalinity of the concrete islost due to carbonation (the reaction of atmospheric CO2 mainly with the Ca(OH)2 butalso with the CSH of the hardened cement paste and the resulting conversion of theOH-which is dissolved in the pore water and causes its alkalinity, into water). It can alsobe destroyed by chloride ions dissolved in the pore water.

Pereira and Hegedus were the first to develop a fundamental model for the effect ofchlorides in concrete [1]. This model has been further developed in [2]. In the presentwork the model in [2] is summarized and supplemented with determination of itsparameters on the basis of experimental results. It is also applied, in combination withprevious results [3,4], to conduct parametric studies, with emphasis on the identificationof measures to increase protection of steel bars from chloride-induced corrosion.

PHYSICOCHEMICAL PROCESSES INVOLVING CHLORIDES INCONCRETE

The source of chlorides in concrete may be internal or external. In the former casechlorides may be present in chemical admixtures (such as accelerators containingCaCI2), in the aggregates or in the mixing water, esp. when beach aggregates or salinewater are used in the mix in coastal or marine construction. The second case, i.e. thatof chlorides entering the concrete from the outside, is more common. In cold climateschlorides may come from de-icing salts, frequently used during the winter over roadsand highways. Concrete in marine structures is continuously in contact with seawaterif it is submerged, or periodically if it is in the splash zone, while in coastal areas theconcrete surface is in contact with air or mist rich in chloride salts. From the surfacechlorides dissolve in the water of the pore system of concrete and penetrate inwards,either by diffusion in stationary pore water or through capillary suction of the surfacewater in which they are dissolved.

Some of the chlorides dissolved in the aqueous phase of the pores chemically react withthe C3A and the C4AF constituents of cement and their hydration products, to formchloroaluminates known as Friedel salts. Others are physically adsorbed on the CSH andthe other (hydrated or not) constituents of the hardened cement paste, while someothers may even by adsorbed on the surface of aggregate particles. In [1] adsorption ofcr of the aqueous phase of the pores by the solid phase of concrete is modeled as aLangmuir process, meaning that it proceeds at a rate which is proportional to the molarconcentration of cr in the aqueous phase, [Cr( aq)] and to the difference between thecurrent molar concentration of adsorbed in the solid phase cr, [Cr(s)], and itsmaximum physicochemically possible, i.e. "saturation", value, [Cr(s)]sat. Chloridesadsorbed or bound in the solid phase, Cr( s), tend to be desorbed and dissolve again intothe pore water. The adsorption-desorption process tends to equilibrium between Cr(aq)

and Cr(s), characterised by an equilibrium constant Keq, equal to the ratio of theadsorption and desorption rates.

In addition to reaching a physicochemical equilibrium with the chlorides adsorbed-bound in the solid phase, those dissolved in the pore water diffuse in it from regionsof high to those of low molar concentration of Cr(aq), according to Fick's first law, atan effective molar diffusivity De,er'

Depassivation of steel bars takes place when the molar concentration of dissolved cr,[Cr(aq)], in their vicinity drops below a certain percentage of the molar concentrationof hydroxyls in the pore water, [OHl The critical value of the [Cr( aq))/[OH-] ratiowhich signals depassivation seems to be around 0.3 [5, 6]. The molar concentration ofOH- depends on the cation type and on whether concrete is carbonated or not. In thecase of NaCl in non-carbonated OPC concrete (in which the pH value is 12.6) thecritical value of the ratio above corresponds to a critical molar concentration of Cr( aq),[Cr(aq)]cr' equal to 13.4 mol/m3, and to a critical NaCl or cr content of 0.75% or0.45% by weight of cement [5]. If the salt is CaC12 instead of NaCl, the critical contentsare about 0.5% and 0.3% CaC12 and cr respectively. These values can be compared tothe maximum accepted cr contents of 0.1-0.4% set by BS81100(1985) and of 0.15%given by ACI 318 (1983).

Corrosion of steel bars following their depassivation requires continuous supply ofoxygen through the gaseous phase of the concrete pores. Hence it cannot take place infully saturated concrete, despite depassivation. Pores which are about 90% filled withwater seem to provide the most favourable conditions for Cr-induced corrosion.

A general model of the physicochemical processes of diffusion-adsorption of chloridesin concrete has been developed recently [2]. The model allows prediction of chlorideconcentration in the solid and the liquid phase of concrete, [Cr(s)) and [Cr(aq)], inmol/m3 of concrete and mol/m3 of pore water respectively, as a function of the initialconcentration, [Cr(aq)L, of the concentration [Cr(aq)]o at the nearest concrete surfaceand the distance x from it, and of time t. For the range of parameter values typicallyfound in practice, the model can be simplified into a nonlinear differential equation for[Cr(aq)] and an algebraic one for [Cr(s)]:

[cr(s)) = dKeq[Cr(s)]S8t[Cr(aq)] (2)

1+dKeq[Cr(aq)]

with initial condition: [Cr(aq)] = [Cr(aq)]j at t=O, and boundary conditions [Cr(aq)] = [Cr(aq)]o at x=o and a[Cr(aq)]/ax=O at the axis of symmetry, i.e. at x=L. Inthese equations De,er denotes the effective diffusivity of cr in concrete (m2/s), Keq the

equilibrium constant for cr binding (m3 of concrete/mol), [Cr(s)]sat the saturationconcentration of cr in the solid phase, c:the concrete porosity and f the degree of poresaturation with water.

Eqs. (1) and (2) differ from the pure Fickian diffusion equation for the total crconcentration usually found in the literature, a[Cr]/at=Decr a2[Cr]/ax2, in that theyalso account for the processes of cr adsorption and binding in the solid phase.

Eq.(1) can be solved only numerically. A simple analytical approximation can bedeveloped, though, for the boundary value problem, if we make the assumption offormation of a moving "chlorination front", where all the adsorption and binding of crtake place at any point in time, and beyond which no effects of the ingress of cr fromthe environment have been felt yet. Then the concentration of Ct( aq) decreases linearlyfrom [Ct( aq)]o at x= 0 to zero at the chlorination front, the distance of which from thesurface, XC\> is given by the expression:

2D CI-[Cr(aq)]oe, tXCI = -------

[Cr(s)]sal

Then, if [cr( aq)]cr denotes the threshold concentration of cr in the aqueous phaserequired for depassivation of the steel bars, and c is their cover with concrete, the timeto depassivation is given by:

[cr(s)]salC2tcr=

2D _[Cr(aq)lo(1- [Cr(aq)]cr)2e,CI [Cr(aq)]o

The accuracy of eq. (4) is acceptable only for values of the externally imposed constantcr concentration at the surface, [Ct(aq)]o' which are of the same order or at most oneorder of magnitude higher than the threshold value, [Cr( aq)]Cf' required for steeldepassivation. In the extreme case of continuous exposure of the surface to seawater,which has a [Cr(aq)]~ value of 590 mOl/m3, and of a threshold concentration, [Cr( aq)]cr'equal to 13.5 mol/m , which corresponds to a [Cr(aq)]/[OH-] ratio of 0.3, consideredtoday as signalling depassivation of the steel due to chlorides [4,5], eq. (4) overestimatesthe time to depassivation of steel bars by as much as 5 times.

Par~met~rs [C~-(s)]sat and Keq can be determined from the slope and the intercept ?fstraight lines htted to test data on the steady-state values of [Cr(aq)] and [Cr(s)] ill

concrete samples with known initial concentration, [Cr( aq)]i [1,2]. Using this techniqueand test results from the literature, the values in Table 1 have been determined.

The dependence of [Cr(s)]sat and Ke on both cement and aggregate content of theconcrete mix suggests that cr are adsofued not only to the constituents of cement paste,hydrated or not, but also, albeit less, to the aggregates. It is reasonable to assume thatthe apparent saturation concentration of cr in concrete, as well as the inverse of the

Mathematical Modeling of Chlorides 169

Table 1. Values of kinetic parameters for different concrete mixes

Tests Concrete composition c; NaCI CaCl2

by w/c a/c fly-ash/c [Cr(s)]sat Keqx102 [Cr(s)]sat Keqx102

(mol/m3) (m3/mol) (mol/m3) (m3/mol)

[1] 0.54 4.57 0.102 239.5 1.24

[1] 0.65 5.85 0.106 214.1 1.64

[5] 0.50 0 0.323 180.2 9.05 601.2 1.30

[7] 0.48 2 0.135 182.6 3.05 432.0 2.64

[7] 0.48 2 0.3 0.152 159.1 2.72 763.5 0.85

[8] 0.50 0 0.292 136.6 6.42 490.2 1.20

equilibrium constant, Ke ' both of which are in mol per unit volume of material, can bedetermined from those of hardened cement and aggregates by applying weighting factorsequal to the proportions of these constituents by volume:

1 1 a f?c--+----Keq,c Keq,a C f?a

w a f?c1+-f? +--

C c C f?a

In Eqs. (5) and (6) subscripts c and a refer to cement and aggregates, f?denotes specificgravity (f?c=3.16 and f?a=2.6) and w/c, a/c are the water-cement and aggregate-cementratios by weight. For the case of NaCI, for which the data are more complete, thefollowing values have been fitted: [Cr(s)]sat c=410 moljm3 of cement, [Cr(s)]sat a=200moljm3 of aggregates, Keq,c=0.03 m3 of cement/mol, Keq,a=0.01 m3 of aggregates/mol.

The most important parameter for cr penetration is effective diffusivity. Values ofDeer derived from the results of tests on fully saturated OPC concrete are presentedin Table 2. The first two values have been derived in [1] taking into account the effectof cr binding, while those in the third and fourth row are obtained herein by fitting eq.(1) to test results in [9,10] as shown in Fig. 1. All other values of Deer in Table 2 areobtained by assuming simple Fickian diffusion (i.e. considering only Deer as thecoefficient in the right-hand-side of eg. (1)), an assumption which is justified on thebasis of the very small thickness of the specimens (3 to 5mm) and the fact thatmeasurements were taken after steady-state conditions had been reached.

170 Papadakis et al

Table 2. Effective diffusivity values for different OPC concrete mixes

Tests by w/c a/c Ep Decrx1012 Decrx1012(m2Is) -concrete- (m2js) -paste-

[1] 0.54 4.6 0.370 3.5 10.60.65 5.8 0.442 8.0 26.1

[9] 0.71 0 0.432 20.0 20.0

[10] 0.5 2.5 0.290 2.0 4.3

[11] 0.4 1 0.247 2.8 4.320°C 0.5 2 0.339 5.5 10.6

28 days 0.6 2.5 0.411 8.0 16.20.4 0 0.247 3.0 3.00.5 0 0.339 8.7 8.70.6 0 0.411 14.1 14.1

[12] 0.4 0 0.229 2.6 2.625°C 0.5 0 0.323 4.5 4.5

60 days 0.6 0 0.397 12.4 12.4

[13] 0.4 0 0.187 1.8 1.822°C 0.5 0 0.286 6.8 6.8

14 months 0.6 0 0.364 18.7 18.7

[14] 0.5 0 0.290 5.8 5.8

Since diffusion of cr takes place only in the pores of the hardened cement paste, theeffective diffusivity values in concrete have been converted to values referring tohardened cement paste alone, by multiplying them by the inverse of the volume fractionof paste in the mix, (l+Qcw/c+(Qc/ga)a/c)/(l+gcw/c). The resulting diffusivity valuesare listed in the last column of Table 2. It is natural to expect that for fully saturatedpores the diffusivity of cr in cement paste is related to the total porosity of the latter,Ep' In fully hydrated OPX Ep can be estimated as [3, 4]:

gc w -0.85c

E =----P w

1+gc-c

Values of Ep from eg. (7), also listed in Table 2, are plotted in Fig. 2 vs the effectivediffusivity of the fully saturated cement paste, De cr p' This figure presents also thecorrelationbetween De,cr,p and Ep derived from the parallel pores model [15]:

ED =-ED

e,cr,p L cr,Hzo

In eg. (10) Dr;r H o.denotes the diffusion coefficient of cr in infinite solution, equalto 1.6x10·9m2/s fof2NaCl and to 1.3x10-9 m2/s for CaC12 at 25°C [16], and L is thetortuosity factor, which depends on the pore structure of the paste. It is proposed here

oE'--" 400

OPC ale = 2.5 w/c = 0.5t = 140 days

o ExpeL results ofHoffmann (1984)

-- This work

200 '\

D='lOI~O".CI - 0 0

00 10 20 30 40 50 60

distance (mm)

Extraction of chloride diffusivity coefficient from test date. by fitting ofthe model of Egs. (1), (2).

30

25

.--... 20UJ---01

E'-"

0' IS0-~U<i 10a

5

00,0

o Experimental results 0

-- Theoretical approximation

OPC20 - 25 DC

Experimental values of chloride diffusion coefficient in ope paste vspaste porosity, and their fitting by Eg. (10),

to consider "[ as the following function of c;p:

Eqs. (8) and (9) fit the experimental data as shown in Fig. 2, if a and m are taken equalto 0.15 and 2 respectively. Then the final semi-empirical expression for Deer in fullysaturated fully hydrated OPC concrete is: '

For partially saturated concrete the effective diffusivity is proportional to a power off estimated from 1 to 3. However, there are not enough experimental data for furtherquantification of the effect of f.

Eqs. (1) and (2), which describe the full model without the "cWorination front"approximation, along with the semi-empirical eqs. (5), (6) and (10) for the modelparameters, were employed to perform parametric studies of the effect of the w/ c anda/c ratios on the ct concentration in pore water in the vicinity of the steel bars. Fig.3 presents the dependence of the evolution of [ct( aq)] with time at x=30mm from theconcrete surface, on the composition parameters, for continuous exposure of theconcrete surface to seawater with a [Cr(aq)] value of 590 mol/m3. Fig. 3(a) shows theextreme importance of the water cement ratio and Fig. 3(b) the lack of importance ofthe aggregate content. When compared with the threshold value of 13.5 mol/m3

corresponding to the [ct( aq)]/[OH-] ratio of about 0.3 which signals depassivation ofthe steel, the [ct( aq)] values in Figs. 3 seem alarmingly high. However these figuresrefer to fully saturated concrete continuously exposed to seawater, which is a case notleading to steel corrosion, as the fully saturated pores block the ingress of oxygenrequired for corrosion of the depassivated steel. The most favourable condition for steelcorrosion due to ct would correspond to concrete in the splashing zone, with a degreeof pore saturation around 90% and an average-over-time value of [Cr(aq)]o at thesurface significantly less than 590 moljm3. It is estimated that this most unfavourablecombination of conditions would correspond to a reduction of the ordinates in Figs. 3by about one half, while in the more usual case of a degree of pore saturation around60% combined with an average [Ct(aq)]o value of a few hundreds mol/m3, the ordinatesof Figs. 3 would be an ordinate of magnitude less. Still under such more favourablecircumstances, avoidance of steel depassivation in a few years time would require a w/ cratio of less than 0.5 and a concrete cover higher than the 30mm (and even higher thanthe minimum of 40mm required by ENV-1992-1 for reinforced concrete in seawaterenvironment) considered in Figs. 3. Fig. 3(a) shows that below the value of 0.50,reducing the w/c ratio is quite effective in delaying depassivation, while theapproximate eq. (4) shows that the time to depassivation increases with the square ofthe concrete cover.

500

, .....,

400 ,,.-,.

/M

~ /

...:::::0 300E'--' ,

u.,,

cr ,~U 200 ,

'--'

100

ope-- t = I yr- - - -- - t = 5 yrs

... t = 10 yrs- ..-.-.- t = 20 yrs

o0,4

,.-,.e-.E--

ope-- t= 1 yr- - - - - - t = 5 yrs......... t = 10 yrs---- .. t = 20 yrs

o -+----.--,--,.---,--.,--." -....---,.--.-----1o 2 3 4 5

Effect of water-cement ratio (a) and aggregate-cement ratio (forwjc=O.50) (b) on chloride concentration at a depth of 30mm from theconcrete surface.

The General Secretariat for Research and Technology in Greece is providing financialsupport to this work.

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8. ARYA, C, BUENFELD, N R and NEWMAN, J B. Factors influencing chloride-binding in concrete. Cern. Concr. Res., Vol.20, 1990, pp 291-300.

9. MIDGLEY, H G and ILLSTON, J M. The peneration of chlorides into hardenedcement pastes. Cern. Concr. Res., VoLl4, 1984, pp 546-558.

10. HOFFMANN, D W. Changes in structure and chemistry of cement mortars stressedby a sodium chloride solutiOn. Cern. Concr. Res., Vo1.14, 1984, pp 49-56.

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14. GAUTEFALL, O. Effect of condensed silica fume on the diffusion of chloridesthrough hardened cement paste. Proc. 2nd Intern. Confer. on the Use of Pozzolansin Concrete, ACI SP 91-48, 1986, pp 991-997.

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