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

Service life design of concrete structures by numerical modelling ofchloride ingress

M.M.R. Boutz & G. van der WegenINTRON, Sittard, The Netherlands

P.E. Roelfstra & R. HaverkortFemmasse, Sittard, The Netherlands

ABSTRACT: A numerical model is presented to simulate chloride ion ingress in concrete structures exposed tovariable climatological conditions. The transport mechanisms of (free) chloride ions are both diffusion throughand convection by pore water. This requires an advanced model for moisture transport in both the saturatedand the non-saturated area. In case that the surface of the concrete structure is in contact with liquid water, therate of the front of the saturated area is controlled by the balance between sorption and diffusion. The chloridebinding isotherm is described by a linear or Langmuir type relation. The salient practical features of the modelare: multi-layer, replacement of layers, imposing a chloride profile as initial situation. The model allows topredict the effect of maintenance actions on the service life of structural concrete, as illustrated for the KingFahd Causeway in the Persian Gulf.

1 INTRODUCTION

Exposure to a saline environment is a major threat tothe durability of reinforced concrete structures. Thechloride ions, present in seawater and deicing salts,penetrate the concrete.At the end of the so-called initi-ation phase a critical chloride content has been reachedat the depth of the reinforcement and corrosion occursat a rate depending on the availability of water andoxygen. The length of the the initiation period is oftenused as a first approximation for the service life.

The transport of chloride ions takes place by dif-fusion through and convection by the pore water.Pure diffusional transport only occurs in the sub-merged zone of marine structures. Where cyclic wet-ting/drying occurs, capillary suction must be taken intoaccount.

In this paper an advanced numerical model ispresented that simulates chloride ingress in struc-tures exposed to cyclic wetting/drying.The multi-layermodel allows to incorporate the effect of maintenance,e.g. applying a coating or replacement by old contam-inated by new concrete. The model has been appliedto decide on the maintenance strategy for parts of thefamous King Fahd Causeway, connecting Saud-Arabiaand Bahrein.

2 IMPLEMENTED MODEL AND OPTIONS

2.1 General

Meijers has developed a computational model to sim-ulate chloride ingress in concrete (Meijers 2003). Thismodel has been implemented in the module CIM-CON I of the software package Femmasse. With thismodel a coupled system of nonlinear differential equa-tions is solved simultaneously for variable boundaryconditions to predict the evolutions of temperature,humidity, and chloride ingress in a 2D space.Althoughconsistent results have been achieved, the model isstill too complex for practical applications. In CIM-CON II the model has been simplified and variousvery practical extensions were introduced.

The limitations and simplifications of this versionare: 1D space, constant temperature and maturity.The principal extensions are: ‘forced’ sorption at awet boundary, easy generation of multi-layers withdifferent properties, replacement of one material byanother at a certain time, options for moisture diffusionmodels, optional inclusion of delayed or irreversiblechloride binding, easy generation of variable bound-ary conditions and storage of material properties in anexplicative material database.

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In the following paragraphs details of the imple-mented models are given.

2.2 Moisture transport models

The principal transport mechanisms of free chlorideions in porous building materials are convection bymeans of a moisture flux and diffusion through themoisture caused by a concentration gradient. To obtainreliable results in the prediction of chloride ion ingress,it is therefore important that the model for moisturetransport is consistent. Advanced moisture transportmodels exist, like that of e.g. Kiessl (Kiessl 1983). Thepractical problem with these models is that many mate-rial parameters must be defined and are often difficultto determine experimentally. One of the objectives ofCIMCON II was to obtain reliable results by means ofa model based on a minimum of measurable mate-rial parameters. The model presented below is animportant step towards this objective.

2.2.1 Desorption isothermA key material property in the moisture models is thedesorption isotherm w{h,T,α}, which describes theevaporable moisture content w as function of moisturepotential h, temperature T, and degree of hydration α(maturity). A desorption isotherm can be generatedfrom the material database for a given concrete com-position, temperature, and maturity. The desorptionisotherm can be linear or piecewise linear based on theimplemented mathematical model (Roelfstra 1989).

2.2.2 Moisture potentialAs moisture potential the macroscopic pore humid-ity h is chosen. The pore humidity is in equilibriumwith the environmental relative humidity as desbribedin (Parrot 1988). This choice, instead of the moisturecontent, is essential in cases of inhomogeneous materi-als and multi-layer systems. More details can be foundin (Meijers 2003).

2.2.3 Diffusion processThe driving force in the diffusion process is thegradient of the moisture potential. The governingequation is:

where qwis the moisture flux in [kg/m2s]; λ is the mois-ture permeability coefficient in [kg/ms] and x is thecoordinate in 1D [m]. The related diffusion equationreads:

where: w is the moisture content in [kg/m3]; t is timein [s]; C is the moisture capacity [kg/m3].

As can be seen in Eq. 2, moisture capacity C is thederivative of the desorption isotherm with respect tomoisture potential h. It should be noted that moisturepermeability coefficient λ depends generally strongon moisture potential h. This relation, however, is notalways known from experimental results. In literaturemore data is available for diffusion coefficient D withunit [m2/s]. If it is assumed that the following relationholds:

then Eq. 1 can be rewritten as:

from which the following relation is obtained:

The substitution of this relation in Eq. 2 results in:

Eq. 6 can be simplified if moisture capacity C is aconstant, i.e. if the desorption isotherm is a linearfunction of moisture potential h. The equation can bereduced to:

which is a “classical” diffusion equation used by manyauthors. Because moisture capacity C is generally nota constant, Eq. 6 is used as diffusion equation inCIMCON II. Diffusion coefficient D depends alsostrongly on moisture potential h. In CIMCON II twooptions have been implemented to describe this rela-tion: Bazant’s model (Bazant 1972) and Mensi’s model(Mensi 1998).

2.2.4 Boundary conditionsBetween the surface of concrete and the surround-ing air generally an interface is defined to describethe resistance for evaporation. Meijers showed thatthe use of such moisture interface elements resultsin poor results (Meijers 2003). That is why in CIM-CON II only the moisture potential can be prescribedon the boundary as well as a no-flux condition to sim-ulate symmetry. A large variety of functions for theprescribed moisture potential can defined by the user.

A difficulty is still the definition of moisture poten-tial h at RH 100 % and a wet surface. Such a situation

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Figure 1. Schematical representation of a sorption experi-ment in a closed containment.

Figure 2. Subdivision of the problem domain in a saturatedand a non saturated area.

occurs e.g. in a simple sorption test (Fig. 1). Accord-ing to the presented model a moisture potential h = 1must be applied at surface A and B, and in the simula-tion the sorption process starts equally from both sides(gravity effects neglected). This behaviour is generallynot observed; the sorption from side B is far moredominant. To overcome this difficulty an option ismade to apply a so-called “forced” sorption boundarycondition. The details of this condition are explainedbelow.

2.2.5 The “forced” sorption boundary conditionAs a first approximation the assumption has been madethat moisture sorption takes place as a sharp wet front.For that purpose the problem domain is subdivided ina saturated and in a non saturated area, as can be seenin Fig. 2.

The moisture flux in the saturated area is defined as:

where qw is the moisture flux in [kg/m2s]; λs the satu-rated moisture permeability coefficient in [kg/m2s];�P the macroscopic capillary suction force [m](height of water column)and x the distance betweenthe wet boundary and the sharp wet front [m].

It should be noted here that sign of �P is alwaysnegative (suction). The basic equation with respect tothe moisture balance for an infinitesimal small timestep dt reads:

where wf = ws − wi is the amount of moisture toobtain saturation [kg/m3] (Fig. 2). in which wi is theinitial moisture content [kg/m3] and ws is the moisturecontent at saturation [kg/m3].

The substitution of Eq. 8 in Eq. 9 and the integrationin time results, after some algebraic manipulations, in:

The results from a sorption test are the penetra-tion coefficient B [m/s0.5], the sorption coefficient S[kg/m2s0.5], and the amount of moisture to obtain sat-uration wf [kg/m3]. The relation between S and B isgiven by:

The penetration equation for sorption conditions reads:

Comparing Eq. 10 with Eq. 12 and considering therelation given by Eq. 11, Eq. 8 can be rewritten interms of measured material data as:

Eq. 13 has been generalised for multilayer systems inCIMCON II.

So far the diffusion process which takes place inthe non saturated area at the wet front and at the oppo-site boundary is not considered (Fig. 2). As sorptionproceeds the moisture flux is slowed down and thesharp wet front is smoothened by the diffusion pro-cess. The penetration depth can even become constantif the moisture flux caused by sorption balances themoisture flux caused by diffusion.

2.2.6 Numerical procedureBecause the spatial and time discretisation for thefinite element method is performed in a standard man-ner it is not explained here. The point of interest isthe method in which the “forced” sorption bound-ary condition is realised. In a time step �t first thediffusion equation is solved for the entire problemdomain (saturated and non saturated area) taking intoaccount imposed boundary conditions (at the wet sur-face h = 1).After this step the elements are “(re)filled”until saturation in a sequential manner from the wet

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border. In the (re)fill procedure the length of the timestep and flux equations are considered.

2.3 Chloride ion ingress model

It is assumed that chloride ions have no influenceon moisture transport and moisture storage proper-ties. Based on this assumption it was decided (froma computational efficiency point of view) to solve thechloride ion ingress problem in a staggered way. Thismeans that in a time increment first the moisture trans-port problem is solved and next that of the chloride ioningress.

The basics of the chloride ingress model of programCIMCON I have also been implemented in programCIMCON II. Only some elementary equations aregiven here.The interested reader is referred to (Meijers2003) for more details.

The total chloride content Ctot (kg Cl/m3 concrete)is related to the free chloride content Cfree(kg Cl/m3

pore water) and the bound chloride content Cbound(kg Cl/kg cement gel) by:

where W is the evaporable water content, ρw the den-sity of water and ξ1 the cement gel content (kg/m3),calculated from 1.25 α times the cement content.

In both CIMCON versions chloride binding can bedescribed by a linear or Langmuir type relation. Inthe case of a linear adsorption isotherm, the boundchloride is related to the free chloride ions by:

Equations (14) and (15) are then combined into:

As mentioned previously, in CIMCON II new optionsfor delayed or irreversible binding are available.

2.4 Validation tests

Validation tests were first performed for moisturetransport by diffusion at constant surface potential.The mathematical solution of the profile is reproducedexactly by the model. The results of capillary suctiontests could be reproduced well too.

In validation runs of chloride ingress in submergedconcrete, it was observed that setting the chloride dif-fusivity k1 in the model equal to 0.9 to 1.0 times theeffective diffusion coefficient (obtained from profilefitting) led to good agreement.

Figure 3. One of the 5 bridges of the Fing Fahd Causeway.

3 APPLICATION TO THE KING FAHDCAUSEWAY

3.1 General description King Fahd Causeway

The King Fahd Causeway is situated in the Persian Gulfand has been in service since 1986. The causeway hasbeen build by the Dutch contractor Ballast Nedam andthe target service life is 75 years. Part of the King FahdCauseway are 5 concrete bridges with a total length of12 km. The bridges consist basically out of piers onwhich pretensioned box girders are resting.

The Gulf region is highly aggressive to concrete.A durability study group was formed by the contrac-tor to formulate appropriate measures. This has led tothe following measures (Heummen 1985, Bijen 1996)with respect to:

• concrete composition:

– application of blast furnace slag cement (slagcontent ≥70%) instead of the specified sulfateresistant Portland cement (SRPC),

– low water/cement-ratio (0.38),– low initial chloride content (≤0.1% of cement

weight)

• structure:

– high concrete cover: 50 or 75 mm, depending onthe exposure zone.

• surface protection:

– epoxy coating in the tidal- and splash zone ofthe piers.

3.2 Salt weathering

The box girders of 3 bridges currently show salt scal-ing. The scaled areas represent less than 5% of thetotal surface of the girders of these bridges. At theselocations a high seawater spray occurs due to the pre-vailing wind and the particular configuration. In these

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Figure 4. Average chloride profiles in 2005 of scaling andnon-scaling areas of the box girders. Note: mc = cementweight.

areas approximately 10 to 15 mm has scaled due to saltcrystallization (Bijen 2007).

It has also been observed that the concrete coverin the scaled areas is locally less than the specified50 mm.

Currently, the following repair procedure is exe-cuted in salt scaling areas: cleaning with sweet water,filling cavities and surface finishing with epoxy resin,followed by the application of an epoxy coating. Thequestion rises if this procedure is sufficient to preventrebar corrosion in the remaining part of the target ser-vice life. An alternative procedure, that is currentlyconsidered, is to remove the outer 20 mm of the saltinfiltrated concrete, to replace it with sprayed con-crete and seal it with a watertight epoxy coating. Inareas without salt scaling only the epoxy coating willbe applied.

3.3 Current chloride profiles

In Figure 4 average chloride profiles in scaled and non-scaled areas of the box girders in 2005 are shown. It isobvious from this figure, that chloride penetration issevere in the scaled area, whereas it is only minor inthe non-scaled area.

The surface concentration Cs and the effective diffu-sion coefficient Deff were determined from the profilesby least-squares fitting using:

where C(x,t) is the chloride content at depth x andtime t, Ci the initial chloride content and erf the error-function. Eq. (17) is derived from Fick’s 2nd law ofdiffusion.

The results of the curve fitting are given in Table 1.The value of the diffusion coefficient in the non-scaledarea is virtually identical to the value (2 × 10−13 m2/s),used in the original durability design of the bridge

Table 1. Results from curve fitting profiles of Figure 4.

Area Cs (% of cement weight) Deff (10−13 m2/s)

Scaling 5.8 3.5Non-scaling 1.4 2.4

(Bijen 1996). In the scaling area the effective diffu-sion coefficient is slightly higher. However, the surfacechloride content is increased by a factor 4 comparedto the non-scaling area.

The near-surface layer in the scaling area is obvi-ously more porous, which can be explained by a lesseffective curing during the production of the prefabgirder and/or by wearing of the surface.

Note that SRPC-concrete with identical water/cement-ratio has a diffusion coefficient of approx-imately 5 × 10−12 m2/s, i.e. more than 1 magnitudehigher than the concrete of the Causeway.

3.4 Model predictions future chloride ingress

Using CIMCON II model predictions have been madeof the chloride penetration in salt scaling areas of thegirders after execution of either the current or alter-native repair method. Based on the results of thesesimulations a rational decision can be made whichprocedure is the best choice with respect to durability.

3.4.1 Input parametersA special feature of CIMCON II is that a chlorideprofile can be introduced as the initial condition of amaterial layer. At the start of the simulations the aver-age chloride profile of a salt scaling area as shown inFigure 4 is imposed. In the current repair method thesurface is sealed with an epoxy coating. The sealingis translated into the model by imposing the bound-ary condition ‘no fluxes’ at the surface. The chlorideprofile will then smoothen out by pure diffusion aftersealing.

In the simulation of the alternative repair method,the first 20 mm is replaced by sprayed concrete with aninitial chloride content of 0.1%. At depths of 20 mm ormore the average chloride profile of salt scaling area ofthe girder is present. At the surface again no fluxes areallowed to simulate the presence of the epoxy coating.

It is furthermore assumed that the existing concretein the girders has a equilibrium moisture potential overthe whole thickness of the member. The transport ofchlorides will then only take place by diffusion. Inthe simulation of the current repair method the pre-diction only depends on the chloride diffusivity andthe chloride binding of the existing concrete. In thesimulation of the alternative repair method chloridediffusivity and binding of the existing and sprayed con-crete are important, next to the depth of removal of the

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Figure 5. Evolution with time of chloride profiles in scaledarea after current repair method (sealing with epoxy coating).

Figure 6. Evolution with time of chloride profiles in scaledarea after alternative repair method. New, sprayed concreteis present in the first 20 mm.

salt infiltrated concrete (assumed to be equal to thethickness of the sprayed concrete).

3.4.2 Results simulationsIn the Figures 5 and 6 the evolution with time ofthe total chloride profile is shown after execution ofrespectively the current and alternative repair method.In the first case the profiles are levelling off with timeby unidirectional inward diffusion. In the latter casethe first 20 mm with high chloride levels are replacedby sprayed concrete with low chloride content, afterwhich the profile in the existing concrete levels off bydiffusion in 2 directions: into the sprayed concrete anddeeper into the existing concrete.

3.5 Risk of corrosion for both repair procedures

A large experimental program performed in theNetherlands (CUR 1992) using a.o. blast furnace slag

cement similar to that applied in the Causeway, yieldeda value of 1.0% of the cement weight for the criticalchloride content. Considering the intensive inspectionprogram performed on the Causeway, it is consideredsafe to use this value for the initiation of corrosion.

It is clear from Figure 5 that sealing the scalingareas with epoxy will prevent corrosion in the next 50years only at high covers (>45 mm). However, afterexecution of the alternative repair method corrosionwill not be initated at covers as low as 20 mm.

4 CONCLUSIONS

The numerical model, implemented in CIMCON II,allows to describe chloride ingress in concrete struc-tures much closer to reality than the currently availablephenomenological models. The effect of maintenaceactions like replacing chloride contaminated concreteby new concrete or the application of a coating orhydrophobing agent, on the service life of the struc-ture can now be incorporated.The example of the KingFahd Causeway illustrates this.

REFERENCES

Bazant, Z.P. and Najjar, L.J. 1972. Non Linear Water Diffu-sion in Non Saturated Concrete. Materials and Structures,Vol.5, Number 25, 3–20.

Bijen, J. 1996. Blast Furnace Slag Cement for DurableMarine Structures. ‘s-Hertogenbosch: VNC/BetonPrisma

Bijen, J. 2007. Report about the performance of the KingFahd Causeway. Confidential report.

CUR 1996. Critical chloride content in reinforced concrete.CUR-report 96-4 (in Dutch).

Heummen, H. van, Bovée, J., Zanden, H. van der, Bijen, J.1985. Materials and Durability. In Saudi Arabia BahrainCauseway. Symposium Delft University of Technology.

Kiessl, K. 1983. Kapillarer und dampfförmiger Feuchtetrans-port in mehrschichtigen Bauteilen. Dissertation, EssenUniversity, Essen, Germany.

Meijers, S.J.H. 2003. Computational Modelling of Chlo-ride Ingress in Concrete. Dissertation, Delft Universityof Technology, ISBN 90-407-2386-9.

Mensi, R., Acker, P., and Attolou, A. 1998. Séchage du beton:analyse et modélisation, Materials and Structures,Vol. 21,2–12.

Parrot, L.J. 1988. Moisture profiles in drying concrete.Advances in cement research, 1(3), July, 164–170.

Roelfstra, P.E. 1989. A numerical approach to investigate theproperties of concrete. Numerical Concrete. Dissertation,Ecole Polytechnique Federale de Lausanne, Switzerland.

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