OARS - Open Access Rewards System
DOI : 10.2240/azojomo0315

Modelling Chloride Ingress into Concrete Part 1 - Background

Laurie Aldridge

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This is an AZo Open Access Rewards System (AZo-OARS) article distributed under the terms of the AZo–OARS https://www.azom.com/oars.asp which permits unrestricted use provided the original work is properly cited but is limited to non-commercial distribution and reproduction.

Submitted: 23rd November 2011
Volume 8 January 2012

Topics Covered

     Service Life
     Methods of Determining Diffusion Coefficients Assuming that Fick’s Laws Control Chloride Ingress
     Penetration Profile
     Through Diffusion
     Simulation of Penetration Profile and Through Diffusion
     Pore Development of Cement Pastes
     Influence of Sea Water on Cement Pastes
Contact Details


Billions of dollars are spent annually to replace defective infrastructure that needs replacement only because of concrete failing to attain its expected service life. Much of this cost is due to the effects of chloride ingress into the concrete removing protective sheaths from steel reinforcement leading to destructive corrosion of the infra structure. Thus accurate prediction of the rate of chloride ingress into concrete would lead to the establishment of specification of an adequate concrete cover to give defined service life.

There have been a number of studies in which the chloride penetration profile of concretes exposed to a chloride solution for different defined periods of time. In this series of papers these data sets were fitted to a consistent simple semi-empirical Fick’s law equations using an excel spreadsheet. The method of fitting appeared to be robust enough so that time dependant chloride profiles could be fit. Such fits can be used to estimate a service life of concrete that is limited by chloride corrosion of the reinforcement steel placed at a defined depth from the surface of the structure.

In this part – the first of a three part series the method of determining the diffusion coefficient from the penetration profile is outlined and contrasted with that using the through diffusion techniques. The service life of concrete is defined here as the time it would take for the chloride to diffuse through the concrete cover in such concentration that removal of the protective sheath from reinforcement steel is initiated. The method of estimating this service life from chloride diffusion is detailed. It is suggested that in concrete chloride diffusion would be different in sea water than in sodium chloride solutions.


Concrete, Durability, Chloride Diffusion, Reinforcement Corrosion, Service life


One of the most costly and common causes in lack of durability in infrastructure is the corrosion of reinforced concrete. The lack of durability in concrete has been identified as a major cost to society. For example Swamy [1] gave the specific example of cost of repair to infrastructure the Midlands link motorway around Birmingham. This cost £28 million to construct. Even though, between 1972 and 1989, £45 million was spent on repairs it is estimated that another £120 million will be required for repair within 15 years. Swamy also estimated that in European infrastructure every year the structural damage and repair bill was about 4 billion euros. These problems are evident world wide. In the USA over 10% of the highway bridges are approaching the end of their service life [2]. Mostly the ending of service life is due to corrosion of reinforcement in concrete initiated by chloride which has penetrated the concrete cover to remove the protective cover on steel reinforcement. Hence it is surprising that while ingress of chloride into reinforced concrete is costing billions of dollars each year durable concreting is not a growth industry. Unfortunately this is not the case for publishing papers on concrete durability which is definitely a growth industry. The problem of chloride ingress was identified in the 1930’s. Then the San Mateo-Hayward Bridge across the San Francisco bay developed significant cracks only 7 years after the 1929 opening [3]. In 1940-1941 four experimental installations of test piling were driven into marine or fresh water environments as part of the long-time study of cement performance in concrete. After 15 years exposure it was concluded 1.5 inches of cover was insufficient to prevent rusting of steel reinforcement and cracking of concrete [4].

Preventing ingress of chloride in reinforced concrete is not simple. Fundamentally only crack-free, good-quality, un-carbonated, concrete must cover the reinforcing. At an absolute minimum it requires the fundamentals of producing quality cover concrete such as

  1. Adequate mixing
  2. Proper composition (with special emphasis both on amount of water and the addition of supplementary cementitious materials to blends with pulverized fuel ash (PFA), ground granulated blast furnace slag GGBFS, or silica fume)
  3. Proper curing
  4. Proper compaction
  5. Adequate cover.

This has not always been achieved. Robinson [5] commented on Australian practise “In the 1970’s and 1980’s, serious problems started to manifest themselves in many reinforced concrete buildings after a relatively short service life. Poor workmanship, cost-cutting or just plain ignorance of good concrete practice {were} the major factors in these premature failures. Costly remediation was required on many of these structures and the concrete industry received a lot of bad publicity based around the theme of ‘concrete cancer’”. Unless such flawed practices have been addressed there is little point in predicting chloride ingress as service lives of less than 10 years can be guaranteed. Hence before industry invests in predicting chloride diffusion it first has to ensure that concrete cover is made from good quality concrete well mixed and having met the conditions of the so called concrete four c’s composition compaction curing and cover. In addition carbonation and cracking of the concrete have to be limited. Obviously the durability of concrete is like a chain where failure of the weakest link leads to failure of the entire structure.

Fagerlund [6] reviewed the specifications of concrete used in the Oresund Link between Sweden and Denmark where a service life of at least 100 years was needed. Based on several documented assumptions he concluded that it was necessary to have a concrete cover of 75mm for a concrete where the water cement ratio was 0.40 and the diffusion coefficient was less than 5*10-12 m2/s (or 150 mm2/year). Similar types of calculations were carried out by Siemes et al [7], who in their paper “Design of Concrete Structures for Durability” suggested that present design methods for durability of concrete were based on rules that did not give objective insight to expected service life and that objective comparison between different durability measures was not possible. Siemes et al concluded that the current methods were unacceptable particularly when lack of durability can lead to loss of human life and high economic loss.

Although catastrophic failure is the most damming indictment of poor construction premature it is costly maintenance that should be identified as the most likely outcome of lack of durability. In 1979 Potter and Guirguis [8] surveyed large (greater than three story) residential buildings erected in the previous 15 years in North Sydney. They found that; 69% of the buildings showed some incidence of durability distress, the younger buildings shown increase frequency of distress than those 10 -15 years old, and that buildings located within 1 km of the coast exhibited more corrosion than those 1-2 km from the coast. In another Sydney survey published in 1990 of 95 buildings Marosszeky and [9] showed that for an average 15-year old building in Sydney the cost of repair the original building represented more than 34 % of the cost of design, fabrication, reinforcement, supervision and placement of the reinforcement steel. These costs are insignificant to those in Canada where it has been estimated that repair of concrete parking buildings would exceed $3 billion dollars [10].

Service Life

Somerville [11] in 1986 suggested a definition of design life as the minimum period for which the structure can be expected to perform its designated function without significant loss of utility and not requiring too much maintenance”. He used as an example the 2-phase mechanism for the corrosion of reinforcement where a time for the aggressive agent to reach and activate reinforcement is defined with the second phase being the time for the aggressive agent to initiate corrosion. For the purposes of this paper service life is defined as the time taken for the chloride to penetrate the cover concrete so that the critical chloride level is exceeded. Following discussions in the literature the illustrative cover used here is taken as 50 mm [12] and the critical chloride level is defined to be a Cl level in the concrete of 0.6 wt% of the binder composition [13]. It should be noted that in this review it is assumed that the concrete materials are free of any chloride impurities.

The motivation for writing this review was to enable Australian infrastructure owners to use reliable predictions of service life limitations as a result of chloride ingress into reinforced concrete. In 2005 the project Chlortest was presented [14] in the Report - Modelling of Chloride Ingress it was concluded that most models are not very accurate is predicting reality. In able to be used by normal engineers prediction models have to be robust and simple to operate with the assumptions clearly visible. Ideally spreadsheet models would be most appropriate.

In the Chlortest [14] project a number of models are tested and loosely they are based on two approaches (i) using Fick’s second law or (ii) the using flux equations. In this review only a very simplified version of the Fick’s law equation is used.

Ideally the chloride profile would be computed from the equation

          C(x) = S (1-erf[x/(2*sqrt{t*D}])      (1)

Where C(x) is the amount of chloride expressed as % of binder x (mm) is the distance from the surface and S the surface concentration of chloride, t the time (years) and D is the diffusion coefficient (mm2/years). Note this can be converted to the SI definition of D (m2/sec) by dividing by ~ 31.5*10-12.

However equation (1) relies on the assumption that S and D is constant dependant on the concrete mix. This is not the case. It has been shown [15] that both S and D varied with time and that this variation could be predicted by a power law where

          D(t) = D0(t/t0)-n       (2)

            S(t) = S0(t/t0)m      (3)

Where t0 is a reference time (generally 28 days or 0.07 years)

The values n and m are powers lying between 0 and 1. Note the difference in signs in equations 2& 3 due to the fact that S increased with time while D decreased with time. In fact it as will be discussed later it is only because of the significant decrease of D with time that concrete can be used in marine waters.

Combining Equations 1, 2, & 3 gives the Fick’s law equation (4) that will be used in the remainder of this report.

          C(x) = S0(t/t0)m (1 – erf(x/{2 sqrt(t D0(t/t0)-n )})      (4)

It is important to realize that this equation is only semi-empirical and should be regarded as tool for fitting rather than a physical equation that can be used to predict exact long term solutions.

Although there is a more rigorous method of evaluation of chloride profile predicted by Fick’s second law given in [15] the cruder approximation given by equation (4) seems to give results which are fit for the purpose of this review.

Somerville [16] has suggested that the basis of a performance plan would be to differentiate the expected service life into periods (in years) represented by; less than 5, 5-10,10-20, 20-40, 40-100, and greater than 100 years. Any model of service life should be able to determine which of these categories the concrete should fit.

Methods of Determining Diffusion Coefficients Assuming that Fick’s Laws Control Chloride Ingress

Chloride is not the only ion for which diffusion coefficients have been determined. The nuclear industry commonly uses cement pastes and mortars to encapsulate radioactive nuclides and there are many determinations of diffusivity of different ions measured through hardened cement pastes. Three common experimental methods of measurement are

  1. Penetration profile of the ions ingress
  2. Through diffusion method where the rate at which the ions move through thin disks (2-6 mm in thickness) is related to the diffusivity
  3. Leaching procedures where the rate of incorporated ions removal by water is related to the diffusion coefficients.

Although the theory relating diffusion to Fick’s laws are well known the interrelation of the diffusivities of Cs and Sr by the different methods was almost impossible. Bertram et al [17] were only able to harmonize the different diffusivities by assuming that the rate of binding of ions to the cement pastes were governed by a rate equation and that only by solving both the diffusion and rate of binding/ release together could diffusion coefficients taken from the different methods be compared. It should be noted that the chloride diffusion is more rapid through cement pastes than both Cs and Sr and in this section it is implicitly assumed that chloride diffusion measured by penetration profiles or by through diffusion methods are essentially the same. No attempt has been made here to describe leaching techniques which is not relevant to chloride transport through construction concrete.

Penetration Profile

Estimating the diffusion coefficients from penetration profiles is the normal way of estimating chloride diffusion in concrete and a typical example of the method is defined by Nordtest (1995) NT Build 443 “Concrete, Hardened: Accelerated Chloride Penetration” where a water-saturated concrete sample which has been cured for 28 days is placed in a NaCl 2.8M/L solution for a fixed time and the chloride profile is fitted by the equation (1) at the time of curing to give estimates of both S and D.

An alternative method of estimating D is given by Nordtest (1999) NT Build 492 Chloride Migration Coefficient from Non-Steady-State Migration. This method essentially based on measurement of penetration profiles after a DC voltage accelerated the chloride transfer for 24 hours when the core was broken open and the position determined from the surface at which the chloride concretion in the concrete is 0.07 Moles/Litre. From this data D was computed for chloride diffusion by a modification of equation 1 from; voltage, time, temperature of the solutions, and the thickness of the specimen. It is important to note that S cannot be estimated from this method and this parameter is critical to predict service life as detailed in the Working Party 4 report in the Chlortest project [14]. El Cherkawi [18] has computed service life assuming that S could have a range of values and in some cases this method would seem to predict service life such that the concrete could be categorised discussed in a previous section.

The importance of time dependence of S and D (equation 2 & 3) mean that curing times must be strictly measured for both determinations. The precision of both methods has been estimated by round robins [19-20].

Through Diffusion

An alternative method to the penetration profile is to calculate diffusion measurement of

Figure 1. Schematic of through diffusion theory parameters

chloride transport through thin discs of concrete. This method is generally used in research on chloride diffusion through cement pastes or mortars. A solution of NaCl is placed in the left hand chamber and another solution (generally NaOH) placed in the right hand chamber with the two chambers separated by a slice of cement paste (typically 2-6 mm thick). Generally both solutions are saturated with Ca(OH)2 to prevent the leach of this material from the slice. The rate at which the chloride is transmitted through the slice is dependant on the diffusion coefficient. The setup is shown in the schematic found in figure 1. The diffusion coefficient D is computed from the equation

          D = m l L/(Cin-Cout)      (5)

Where; A the area of the paste slice, L the length of both the diffusion and reservoir chamber, Vout is A*L, l is the thickness of the slice, Cin is the concentration of the NaCl in the reservoir chamber at the experiment end, Cout is the concentration of the NaCl in the diffusion chamber at the experiment end, and m is the slope of the line dCout/dt


  1. that if l & L are both measured in mm and t in years then D is in mm2/years,
  2. that normally there is a significant delay before the chloride breaks through and this tbr (time of breakthrough) is related to the binding of the chloride ions to paste

The use of the through diffusion to measure Cs+ diffusion coefficients in cement pastes with and without zeolites has been published [21]. There the zeolites bound the Cs and it was possible to see effects of increasing binding (by addition of zeolites) and increasing the Cs transport by heating the cement which is believed to lead to larger capillary pore in cements. The effects on the through diffusion measurements are shown in the figures 2-10 in this publication and give some insights into the types of behaviour expected if the chlorides would be permanently bound to the cement pastes as Cs is known to be bound to the zeolites by an ion-exchange type of reaction. Bertram et al [17] have shown that for Cs and Sr both the binding and the kinetics of binding are important factors that must be considered when trying to predict the transport of these ions through cement.

Simulation of Penetration Profile and Through Diffusion

In order to assist in planning experiments the expected penetration profiles and through diffusion results were modelled assuming D= 32 mm2/year and S= 3.5 using GNU Octave programs (which can also be run on Mathlab) The results for the calculation of penetration profiles as a function of time are shown in Figure 2-4. The calculated penetration at different times in shown in Figure 2.

Figure 2. Penetration Profiles (D= 32 mm2/year, S=3.5 Cl %wt binder) at 0.06, 0.12, 0.25, 0.5, 1, 2, 4, 8, 16, 32, 64, & 128 years.

From the results shown in Figure 2 it is possible to compute the chloride concentration at 50 mm concrete cover as a function of time. This relationship is shown in Figure 3 and from this figure if it is assumed that chloride will corrode steel when the chloride concentration is greater than 0.6% (with respect to the binder) then it can be seen from Figure 2 that the concrete structure will have a design life of more than 20 years.

The through diffusion concentrations of chloride (Figure 4) were modelled for a 2mm thick cement paste in a 30 mm long reservoir and diffusion chamber for pastes with diffusion confidents of 95, or 315 or 3150 mm2/year. Using this program it was easy to show the difficulty of using this method for concrete of reasonable thickness while confirming that for most pastes the method gives acceptable chloride concentrations so that D could be easily measured. However it should be noted that in this method S is not used in the equations and comparisons between the diffusivity measured by through diffusion with those measured by penetration profiles may offer an insight into correct modelling of chloride ingress.

Figure 3. Cl concentration as a function of time at cover depth 50mm. (D= 32 mm2/year & S=3.5)

Figure 4. Comparison of Cl concentration with time in through-diffusion experiments under conditions described in the text.

In practice there are many different methods of estimating the chloride diffusivity and all use severe approximations. However the basic approximation that all of the methods discussed here is that it is assumed that the concrete is water saturated and that this will be the “worst case” for the magnitude of chloride transport. While this is the undoubted truth in the vast majority of cases it is possible that specific problems this assumption may not be justified. For example if concrete is placed in a tidal zone where it is both wet and dry every day and also dried out by persistent strong winds it is possible to envisage cases where the chloride may in fact be more rapidly transported than in submerged concrete exposed to sea water.

However Cl transport may not be governed by diffusion as suggested by Volkwein [22] who found that hydration suction could dominate chlorides transport into concrete. Such an event would occur when concrete was cured sealed and then placed in water. While this should not take place when concrete is contacted with sea water Volkwein [23] reviewed corrosion initiated from de-icing salts in concrete structures where the diffusion model was not relevant to the chloride ingress.

It has been shown that both D and S are time dependant and should be actually written as D(t) and S(t). The time dependence of D will be influenced by the transport of water into cement paste is governed by the size and extent of the continuous capillary pores and that as hydration proceeds then the pores will close. Thus pore development of the setting cement pastes will influence chloride ingress.

Pore Development of Cement Pastes

Bordallo et al [24] have reviewed the effects of hydration of cement pastes on the closure of capillary pores and the effect this has on restricting water transport in cement pastes. Based on the Powers-Brownyard model cement paste consisted of 5 components unhydrated cement, gel solids, gel water, capillary water and an air void formed by chemical shrinkage. Chemical shrinkage occurs because the volume of the hydrated gel is less than the volume of the cement and water.

Assuming that the cement pastes were cured in a sealed environment so that no extra water was added and the standard volumes of the reactants they used an excel spread sheet to plot the volumes of capillary pore and chemical shrinkage as a function of alpha the degree of hydration. As a rule of thumb it can be considered that at 28 days alpha is about 0.75 (or that 75% of the cement had hydrated).

It was considered that the capillary pores had a pore diameter greater than 10 nm and that for a paste of w/c ratio of 0.42 the capillary pores became discontinuous after 7 days curing while for a paste with w/c of 0.8 capillary pores were always continuous. The volume fractions are shown in Figure 5. Note that there is a considerable volume of water in the gel pores but that as much of the pores are about 2nm in diameter most of this water is constrained.

Obviously in well made but poorly cured concrete; the diameter, extent, and amount of discontinuous capillary pores in cement pastes will govern the rate of transport of water and ions. Hence both curing (which increases the degree of hydration) and water / cement ratio dominate water transport when the paste is not cracked. In the case of blended cements the term water / binder ratio is generally used instead of water /cement.

It should also be obvious that in well made and well cured concrete with minium water to cement ratios that it will be the transport of the chloride through the gel pores that would govern the transport of the chloride in pastes. The motion of water in the capillary pores has been the focus of Bordallo et al’s research. It is the hindrance of the chloride ion in the restricted gel pores that in fundamental to chloride transport.

Figure 5. Volume of Components of hydrated cement pastes as a function of degree of hydration (alpha). When cement is 75% hydrated (1) at w/c =0.42 6% of the volume is chemical shrinkage void and 14% capillary pores and (2) at w/c =0.8 4% of the volume is chemical shrinkage void and 43% capillary pores.

There is binding of chloride ions to the cement pastes [25-28]. The effect of this on the penetration profile is not understood but has been “allowed for” in some calculations. Because of the complexity no attempt has been made to model this effect in this review despite the belief it may significantly alter amounts of chloride allowed into hardened cement paste. Such an effect may significantly change the diffusion coefficients but is not evident from the quality of the fit to the penetration profile while it may have significant effect on the prediction of future chloride ingress. It can be considered that there are two types of binding of chloride ions to the pastes. The first is in the double layer adjacent to the paste surface. Here as it is considered that overall the paste surface is negatively charged that cations such as K+ and Ca2+ are attracted to the surface. These cations in turn will attract the negatively charged anions SO42- Cl- and OH-. This is in contrast to the second postulated method of binding where formation of Friedal’s salt (which has a positively charged surface) attracts and binds to the negatively charged anions SO42- Cl- and OH-.

The competition of anions for the binding sites will ensure that the amount of chloride binding will be determined by the chemistry of the pore water. Thus different cement compositions which have different pore water compositions may have significant reduction of rate of ingress of chloride in their pastes. The importance of the anion charge of chloride was shown by Yu et al [29] who measured the relative diffusion of oxygen to chloride as the pores of pastes were closed by hydration. Both oxygen and chlorides were dissolved in the pore water and it was found that there was no simple linear relationship between the two diffusivities. Dissolved uncharged oxygen was more mobile than the negatively charged chloride ions. As the pores closed during hydration the chloride transmission decreased more than that of dissolved oxygen.

Influence of Sea Water on Cement Pastes

It has been shown that seawater greatly modifies both the composition and pore structure of cement pastes in concrete and mortars [30-31]. Polder and Larbi [31] compared three different concretes that had been exposed to the North Sea for up to 16 years and measured the surface profiles of S, Mg, Na and K. However no C profile was measured and this may have given some significant information as carbonation is possible in the sea water.

It should also be considered that any Ca(OH)2 (Portlandite) in the surface layers of concrete should be leached away on exposure to the sea for prolonged periods. All of these factors suggest that there will be considerable modification at the concrete surface which may in fact inhibit the ingress of chloride after a number of years. Such modifications can be considered to change the composition which may be why in some concrete the chloride surface drops. When this happens in fitting penetration profiles it is common to not fit any surface anomalous values.

It the above speculation is true and seawater does reduce the amount of chloride ingress through a “skin” on the concrete surface then it would be necessary to use exposure in seawater rather than NaCl to estimate the chloride ingress. It is noted that Bai et al [32] used synthetic sea water and that this may be a fruitful area to follow up. However it must be realized that the concentration of sea water to concrete may be critical. For example if the concentration of carbonate in sea water is very small continuous exposure of concrete to the same water will soon exhaust the carbonate which in real seawater would be continuously refreshed. Similarly the concentrations of S and Mg may be of importance.

It should also be noted that that there will be considerable differences between synthetic sea water and real sea water. Firstly Lindvall [33] measured different chloride ingress into the same concrete in different parts of the world (including Australia) and attributed the great differences in the penetration mostly to differences in the temperature of the water and differences in the concentration of chloride ions in the different sea waters. Secondly fixed quantities of chemicals will become depleted (unless they are replenished) on continuous exposure to concrete while concrete in the sea will be faces with the same concentration. Also synthetic sea water may have a different speciation to real sea water. (Yet unpublished work in this laboratory using Phreeqc [34] did find only minor differences between the calculated speciation of the two waters.) The effect of sea water on concrete exposed to sea water for either 8 months or seven years in the Sea of Japan has been compared for concretes made from OPC PFA and Ground Granulated Blast Furnace Slag (GGBFS) by Torii et al [34]. The effect on the concretes is both significant and significantly different for different concretes.


These are given in Part 3 of the paper

Contact Details

Laurie Aldridge
Monitoring for Assurance of Durability,
24 Balmer Cres,

E-mail: [email protected]

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