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DOI : 10.2240/azojomo0317

Modelling Chloride Ingress into Concrete Part 3 - Success and Limitations

Laurie Aldridge

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Submitted: 23rd November 2011
Volume 8 January 2012


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 work accurate modelling of chloride ingress to concrete has been demonstrated. One example where the concrete was treated so that there was some sealing of the pores to resist chloride ingress could not be fit using the simple semi- empirical Fick’s law equations. It was speculated that in this case the sealant inhibited curing and when breached allowed the ingress of salt water by hydration suction.

Generally it was shown that for up to ten years ingress equations derived form diffusion can fit the penetration profiles of chloride ingress in sea water. However the classical diffusion model of NaCl ingress into concrete is not adequate to extrapolate so that accurate estimates of service life can be made even up to 50 years.


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


In the first part of this series of papers the classic simplified version of the Fick’s law equation was introduced where 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 this relied on the invalid assumption that S and D is constant whereas both S and D varied with time as described 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.

A combination of Equations 1, 2, & 3 gives the Fick’s law equation (4) t

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

In the second part of this series a number of chloride penetration profiles which were taken as a function of time were fitted to the equation (4) and most of the data could be shown to fit equation (4). On anomaly was the data taken from concretes whose surfaces were treated so that the concrete was sealed from the chloride penetration.


Modelling Chloride Ingress

The accurate modelling of chloride ingress to concrete by equation 4 has been demonstrated in the previous parts of this review. It was found that generally the penetration profiles for chloride could be modelled as a function of time using equation 4. However the examples used had a limit of up to ten years ingress equations. It was also noted that the equation was semi-empirical.

As discussed earlier in this series it would appear that accurate fitting with time can only be carried out assuming that power law equations hold. As far as the reviewer is aware there is little scientific understanding as to why both S and D vary with time in such a fashion. While the capillary pore closure (as was reviewed in Part 1) does explain why chloride transmission will be increasingly inhibited with time there have been few attempts at explaining why the diffusivity falls following equation 2. The plot of both D(t) and S(t) with time from the fitted parameters (table 5 Part 2 of this series) of the data of Lee and Chisholm [43] is shown in Figure 10. It is evident that significant changes in both D and S after 10 years. These can cause significant variations in service life estimates as is shown in table 6 where about a factor of 2 is added to the estimates of service life. There is little understanding about the causes of this variation it should be considered unwise to rely on any improvement in service life that results from the extrapolation of the power law fits beyond 10 years. The results fitted in the earlier Part of this series suggests that S and D do vary according to equations 2 & 3 for periods of ten years. It is recommended that the value of S and D computed at 10 years should be the limiting values used in service life prediction.

The results presented in later and in earlier sections do seem to indicate that at 70 mm cover OPC would, in most cases, have a service life of less than 100 years. However the supplementary cementitious materials do seem to exceed this service life which suggests that ground granulated blast furnace slag and PFA should give significantly more resistance to chloride ingress than do Ordinary Portland Cements.

Figure 11. The effect of the water/ binder of concrete on the diffusivity of chloride. All of the concretes were made from Portland Cements without the presence of supplementary cementitious materials. All of the data were taken or corrected so that the diffusivity coefficient was given at a time of 28 days.

Table 6. Differences in estimated service life of concretes DC400 and GP325 calculated where using different values of the time at which S(t) and D(t) computed by equations 2 & 3.

Years at which D(t) and S(t) are computed DC400 GP325
1 21 13
5 40 21
10 60 25
50 > 100 39
100 > 100 47

Some workers have suggested that prescriptive formulations could be made so that concretes could be classified according to their properties and water to cement ratios and then literature values of D0 (t= 28 days) could be used to predict the chloride diffusion. Such an approach was suggested by the fib group [44].

To test this assumption the results from Part 2 of this series of D0 from concretes made from Ordinary Portland Cement were plotted against the water/binder ratio. Other results from literature [45-47] were added to the plot of diffusion coefficients of chloride ions at 28 days (Figure 12). The plot suggests that the errors resulting from this approach would make very unreliable estimates of service life. The results suggest that cements prepared in different countries and under different conditions have such varying properties that this prescriptive approach to service life would be unreliable.

Figure 12. The effect of the water/ binder of concrete on the diffusivity of chloride. All of the concretes were made from Portland Cements without the presence of supplementary cementitious materials. All of the data were taken or corrected so that the diffusivity coefficient was given at a time of 28 days.

Service Life

In Part 1 of this series it was stated that 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. While this ideal can perhaps be realised it is important to note that accurate prediction of transport of chloride in concrete exposed in sea water is limited as

  1. Diffusion equations may not be strictly accurate
    • Chloride diffusion coefficients depend on both the concentration of chlorides and the other cations present in the cement pores,
    • Bound and free chloride in the pores is not fully understood.
    • Seawater modifies the skin of the concrete and this modification cannot easily be modelled nor at present is it understood.
  2. The change of both D and S with a function of time has been modelled by an empirical equation but as yet no compelling physical reasons for the curve have been given. Hence the equations such as equation (4) must be regarded as semi-empirical and it would be very dangerous to extrapolate the diffusion equations outside the time zones of experiment.
  3. Different exposure zones do have different rates of chloride ingress. Many zones are defined with such definitions as splash, tidal, submerged and even exposed to an atmosphere within a certain distance from the coast.
  4. Oxygen must be present at the reinforcement boundary for steel corrosion to occur and it has been shown that in deep-sea corrosion is inhibited by oxygen starvation [49].

These reservations and cravats make it imperative that the approximations behind estimations of service life be made clear. Furthermore although commercial “state of the art” prediction models are available they are must be deemed useless to both the engineer and the concrete structures owners if the predictions from these models are based on assumptions hidden deep within the model whose implications only the modeller can appreciate.

It is only when clear assumptions are made can modelling produce believable limits to chloride transport such as were used for the Concrete Specification for the Oresund Link [6]. While accurate predictions may be almost impossible the work highlighted by this review does suggest that penetration profiles can be adequately modelled by equations 2-4. This suggests that making the proper approximations it is possible to compute “lower limits” of service life of reinforced concrete exposed to sea water. Work has been started on defining such a method with the calculations based on Excel Spreadsheets so that the method will be simple enough for most engineers to use.

Recommendations for Future Work

Arising from the preceding discussion there are fundamental questions that have to be understood in order to reliability predict chloride transport in concrete. In addition; the ability of the cement to bind chloride ions, the effect of sea water on altering the cement paste in concrete, the role of the supplementary cementitious materials in altering the structure of cement paste, and the effect of carbonation of the cement paste on the chloride diffusion all need to be understood in order to progress the technology. It is considered that research should be undertaken so that we are able to;

  1. Understand why S & D varies so greatly with time
    • The variation of S makes little sense unless the surface pastes are changing at a time scale that is different to the binding of chloride to the paste. S variation is significant in years while chloride binding is at equilibrium in days. In particular it would be helpful if we could understand the differences between the pastes made from different blends
    • The variation of D varies appears significantly different to the variation with time of pore structures. Why is this so? It could be that further work based on Yeih [49], Hansson’s [37,38], Tritthart’s [27] and Page’s groups studies [29,36,39,50] on through- diffusion would give important insight into this variation.
  2. Understand the role of supplementary cementitious materials in reducing chloride ingress. There are significant differences between the time dependant chloride ingress in pastes both OPC and blends of OPC made from silica fume, GGBFS, PFA & Meta kaolin. (The literature data from meta-kaolin blends chloride diffusion reaction is very puzzling as if the variation is due to the aluminium then it would be expected that meta-kaolin would be better than PFA which does not appear to be the case)
  3. Understand the effect of ground calcite on chloride in pastes. The production cements in Australia now contain inter- ground calcite it would be of interest to know if this replacement significantly changed the rate of ingress of chloride.
  4. Better understand the binding of chloride to cement pastes and ensure such binding does not effect the diffusion equations as found in the diffusion of Cs and Sr in cement [17].
  5. Better understand the effect of sea water in modifying the surface of pastes and what effect this has on the chloride ingress. In particular it would be helpful if we could understand the differences between the pastes made from different blends
  6. Investigate methods of cost effective determinations of chloride ingress in-situ. Service life predictions depend on the assumption that concrete samples cured in the laboratory will have the properties as the concrete cured in the field. Dewar [51-52] defined real-crete as concrete being made and poured on a construction site and lab-crete as the concrete produced under ideal conditions in the laboratory. He suggested that there were considerable variations in properties between these concretes and also between them and cover-crete which is the concrete on the surface of the concrete which is the zone of poorer quality concrete shielding the reinforcement from the chloride. As laboratory concrete would be expected to have better properties than real-crete there can be substantial differences between the “trial mixes”, real-crete and the cover- crete produced in the field.
  7. Better understand the role of carbonation and drying off cement paste on the ingress and transmission of chloride ions. It has been reported by Ngala and Page [50] that carbonation and drying alter mature hardened cement paste so that orders of magnitude changes are made to the chloride diffusion. This could be a major pitfall in service life prediction where the concrete is exposed to an atmosphere that allows carbonation and drying. Indeed it was speculated earlier in this review that wetting and drying could be an extra “driving force” allowing faster chloride ingress.
  8. Better understand that time that it takes for the chloride corrosion to occur after the chloride has reached a critical level. It has been assumed in this work that the critical chloride level at which corrosion is initiated is defined to be 0.6 wt% of the binder composition [13]. Such an assumption may not be warranted and works by Bamforth[13], Frederiksen[53] and Page[54] should be consulted on the difficulties in making this assumption.


This review on the modelling of chloride ingress into concrete suggests that under the correct conditions it is possible to calculate a service life of concrete exposed to chlorides which can corrode reinforcement steel. The model specifies the depth of the cover over the bar, the time of exposure of the concrete, and needs accurate time dependant values S(t) and D(t) to fit an equation derived from Fick’s laws. The basis of the equation is semi-empirical.

There are a large number of assumptions that have to be made in application of the model and such assumptions should always be made explicit it should be possible to compute a lower limit to service life that is realistic. It is suggested that:

  1. The properties of different cements cause concretes to have different rates of chloride ingress and it must be regarded as the height of folly to predict service from chloride diffusivity from overseas databases.
  2. S and D vary with time according to the power laws represented by equations 2 & 3. It is suggested that the limits at 10 years be used to compute service life.
  3. Chloride profiles in concretes in sea water can be fitted. Such fits should be regarded as semi-empirical and only be trusted within the time frame of the experimental data.
  4. Fitted values of laboratory tested specimens exposed to NaCl solution may not have the same Cl diffusion as the same samples exposed to sea water or exposed to synthetic seawater.
  5. Samples taken from a laboratory are likely to have very different properties to concretes cast into a real structure.
  6. Effects of carbonisation and drying should be investigated further.


This review arose out of work carried out in collaboration with (1) Associate Professor Helosia N. Bordallo (Niels Bohr Institute University of Copenhagen Universitetsparken 5 2100 Copenhagen) on the transport of water in cement pastes (2) work with UTS and ANSTO on measurement of chloride ingress into Australian concrete samples (3) work with David Pollum in the Monitoring Applications of Durability Project (4) work carried out at ANSTO on measuring diffusion through concrete. My thanks go to my collaborators; Heloisa Bordallo, David Pollum, Kirk Vessalas, Kapilia Fernado, Max Da Costa, Paul Thomas, Abhi Ray, Alen Jajou & Mustafa El Cherkawi W.K. Bertram P. Rougeron, K. Harder and V. Patterson.

It should be noted that other excellent studies have been made on chloride ingress and the author of this Australian study is particularly indebted to work of Tang, Nilsson Frederiksen & Mejlbro for whose numerous publications the concrete community owes a considerable debt of gratitude.

Thanks are due to AINSE Ltd for providing financial assistance (Award No AINGRA09104 for Life-span prediction of cement based construction materials) and to D.H. Aldridge for substantial finance assistance for travel.

Finally thanks go out to the wonderful librarians at both the ANSTO and the Cement Concrete & Aggregates Australia libraries for their patience and assistance in locating some very hard to track down references.


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Contact Details

L.P. Aldridge
Monitoring Applications of Durability,
24 Balmer Cres Woonona,
NSW 2517

E-mail: [email protected]

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