Applications using measured values of the transport properties of concrete I: predicting the durability of reinforced concrete
Abstract
The transport properties control the durability of concrete and, in particular, the corrosion of reinforcement. The mechanisms for this are discussed and experimental measurements of corrosion using linear polarisation are presented. These are then correlated with a number of transport related properties. The use of the Nordtest NT Build-492 and the ASTM C1202 electrical tests for predicting corrosion is then considered. It is shown that the Nordtest suffers from the same problems as the ASTM described in Chapters 10–12. However, it is concluded that durability models such as the NRMCE Life-365 model have similar problems so the data from the tests could possibly be suitable for them.
Key words
reinforced concrete; durability; corrosion of reinforcement; NT Build-492; durability models
13.1 Introduction
By far the most common application for data on transport properties is the prediction of the durability of reinforced concrete. While there are some types of deterioration such as freeze–thaw or sulphate attack which affect the concrete itself, most damage occurs through corrosion of the reinforcement. This chapter considers the two main methods used to predict corrosion from transport properties. The first is simply to attempt to correlate corrosion with various transport measurements and the second is to develop predictive models, normally based on diffusion of chloride ions.
13.2 Controlling parameters for concrete durability
Having defined the transport processes in earlier chapters, the key questions are how they may be controlled and how they will affect the durability of a structure. In Fig. 13.1, the left hand column shows a number of factors which we may expect to affect the properties of concrete. They do not, however, directly affect the transport properties and the next column shows the actual internal properties which they are likely to affect. These include micro-cracks, the chemistry and also the ‘formation factor’ for the pores which is a measure of how many direct paths there are through the pore structure. The third column shows the transport properties and the final column shows the deterioration processes that we want to inhibit. Thus we change something in the left hand column in the hope that it will affect the next two columns and finally get a result in the last column. The complexity of this situation explains why it is so difficult to achieve durability in a structure. For structural analysis, the relationship between what we do and the results that we get is defined by quite precise equations. For durability, even moving from one column to the next in the figure is unfortunately only possible by using experimental data which is often difficult to interpret. There are, however, numerous significant relationships on the figure which may be exploited.
The dashed line arrows start from the water to cementitious (w/c) ratio and the curing conditions. If the water content is kept low, this will reduce the number of capillary pores that contain it and the overall porosity will be reduced. Similarly good water-retaining curing will promote full hydration and the resulting products will fill many of the pores and reduce the porosity. Following across the figure shows that this will reduce the pressure-driven flow and the diffusion. The pressure-driven flow then causes frost attack (in combination with capillary suction) and diffusion is a key mechanism in reinforcement corrosion by carbonation or chloride ingress.
The thin solid arrows show that the cement type will be the major factor determining pore fluid chemistry. In particular, the use of a pozzolanic material such as pulverised fuel ash (PFA) or silica fume (SF) will reduce the amount of hydroxyl (lime) and alkali ions in solution. These are the main charge carriers and therefore the electromigration will be greatly reduced. The key effect of this is to reduce corrosion of reinforcement because this depends on the electromigration of these negatively charged ions from the cathode to the anode so they can combine with positive metal ions.
The thick solid arrows show that the cement type will also be the key factor in determining the chemistry of the cement matrix that forms the structure of the hydrated paste. In particular, if a sulphate resisting cement is used there will be few aluminates in it. This will, in turn, severely limit the ability of the matrix to adsorb chloride ions and they will thus remain free to cause corrosion.
There are very many other links in the figure; indeed, almost every factor in each column affects every factor in the next one to some extent and exploring each of them reveals methods that offer the potential to be exploited to improve durability.
It may be seen from the discussion above that reducing transport processes will normally improve durability. An exception to this is the deterioration of saturated concrete in fire. The Channel Tunnel linking England with France experienced a severe fire and photographs of the damage remarkably reveal apparently undamaged reinforcing steel with virtually no remaining concrete. In this incident, the exceptionally low permeability of the concrete prevented the escape of steam from the pores of the saturated lining segments and caused them to literally explode. This phenomenon may be demonstrated by placing very low permeability concrete in a microwave oven. The only solution to this that is known to the author is to mix the concrete with polypropylene fibres that melt at high temperatures and provide pathways to vent the steam.
When considering Fig. 13.1 it must also be observed that building structures with concrete with low transport properties is of no use at all if the depth of the cover layer is not maintained. If the reinforcement is just a few millimetres below the surface, nothing will protect it from the external environment.
13.3 Measuring corrosion of reinforcement
13.3.1 Theoretical analysis
The corrosion experiment is shown in Fig. 13.2. The secondary electrode was mild steel. The concrete samples were also used for resistivity measurements (see Section 8.4.2 for sample dimensions) by applying an alternating voltage between the steel bar in the sample and the secondary electrode. The potentiostat is basically a power supply, but a complex device is needed because the reference electrode can only be used for measuring voltages, not applying them. Thus the potentiostat applies voltages to the secondary electrode while controlling them with measurements from the reference electrode.
Figure 13.3 shows the equivalent circuit for a steel corrosion sample. The anode and cathode both occur at the surface of the steel inside the concrete. The concrete resistance occurs in the thickness of concrete between the steel bar and the salt solution in the tank. The external voltage is measured between the reference electrode and the top of the steel bar in the concrete. The external current Ix flows through the secondary electrode.
The electrochemical process at the anode involves the dissolution of Fe++ ions into the pore solution. The relationship between the voltage across it and the ionic current is assumed to be logarithmic as in equation (13.1):
[13.1]
[13.1]
where:
ϕa0 is the exchange voltage which would occur across the anode if it was in isolation
Ia0 is the exchange current which would flow equally in and out of the bar in isolation and
B1 is a constant known as the Tafel constant.
The electrochemical process at the cathode is the formation of hydroxyl ions from oxygen and water and will similarly be logarithmic as in equation (13.2):
[13.2]
[13.2]
where:
ϕc0 and Ic0 are the cathode exchange voltage and current and
B2 is a second Tafel constant.
If there is no external applied voltage the voltage is known as the rest potential E0 and the current flowing round the ‘loop’ is the corrosion current Icorr which would occur in normal conditions in a structure. Thus:
[13.3]
[13.3]
Thus subtracting from equations (13.1) and (13.2):
[13.4]
[13.4]
But when x is close to 1, x − 1 ≈ Ln(x). Thus, when Ia and Ic are close to Icorr:
[13.5]
[13.5]
With the following definitions:
[13.6]
[13.6]
and
[13.7]
[13.7]
equation (13.5) reduces to:
[13.8]
[13.8]
Equation (13.8) is known as the Stern–Geary equation (Stern and Geary, 1957) and enables the polarisation resistance and thus the corrosion current to be measured by applying an external voltage ϕ close to the rest potential E0 and measuring the resulting external current Ix. This is known as linear polarisation resistance measurement because of the linear relationship in equation (13.8).
A correction is needed because, as may be seen in Fig. 13.3, the circuit also flows through the concrete resistance. This must be measured separately and subtracted from the polarisation resistance. There is also an effect of the double-layer capacitance of areas of the bar that are not corroding. This causes a high initial current to flow but may be avoided by waiting 30 s after applying the external voltage before measuring the current.
13.3.2 Experimental procedure
Samples containing a mild steel bar were placed in salt solution and the initial corrosion rates were measured by linear polarisation resistance measurements. The steel was then polarised to + 100 mV relative to a standard calomel electrode for 28 days and the corrosion rate was measured again. The resistivity measurements described in Section 8.4.2 were used to correct for the concrete resistance.
13.4 Correlating transport measurements with corrosion
13.4.1 Sample testing
Samples were prepared using the mix designs and curing conditions given Section 8.2. The corrosion current was measured and measurements were made of the properties known to influence it (the predictor properties). These predictors were all transport properties except for the lime content and the cube strength. The testing programme is summarised in Table 13.1.
Table 13.1
Summary of experimental programme
| Predictor measurements | ||
| Chloride transport | Concentration (Cl conc) | Measured in sample after gravity assisted ingress (see Section 8.4.3) |
| Carbonation (see Section 8.4.1) | Strain (Strain 18) | Measured on mortar prisms with LVDT |
| Prism depth (Depth 18) | Measured with phenolphthalein at 18 days exposure | |
| Mortar depth (Depth 28) | Measured with phenolphthalein at 28 days exposure | |
| Oxygen transport | Permeability (K(O2)) | Measured on sections on mortar cores (see Section 8.5) |
| Vapour transport | (Vapour) | Measured on thin discs of paste (see Section 8.6) |
| Electrical conductivity | (Conductivity) | Measured between steel and solution on corrosion samples (see Section 8.4.2) |
| Lime content | (Lime) | Measured with thermogravimetric analysis of paste samples |
| Compressive strength | (Cube strength) | Measured on 100 mm cubes |
Predictor measurements are as shown. Corrosion current was measured at the start of the testing programme and at 28 days.
In addition to the carbonation strain measurements described in Section 8.4.1, the carbonation depth was measured by breaking the samples and spraying phenolphthalein indicator solution on the exposed surface to show the areas of reduced alkalinity. The lime content was measured by thermogravimetric analysis of ground samples. The area of the calcium hydroxide peak which occurs at around 450 °C was recorded (Cabrera and Claisse, 1991). Two readings were obtained for each sample condition for each experiment.
13.4.2 Statistical analysis
Initial calculations
For a statistical interpretation of regression and analysis of variance, it is assumed that the data are normally distributed. The results obtained for corrosion currents were very clearly non-normal and thus unsuitable for analysis. Equation (13.4) indicates that the rest potential is proportional to the log of the corrosion current (and this was observed for this data). This logarithm was found to be normally distributed and was therefore used as the fundamental parameter and, on this basis, it was used for the analysis.
Regression
The purpose of the regression analysis was two fold:
1. to construct a model for predicting corrosion current from the measured predictor properties, thereby identifying which properties provide the best indication of corrosion;
2. to assess the size of the effect of each predictor property on corrosion current.
A particular property may be highly correlated with corrosion current yet may have little actual effect on it. This is the distinction between the correlation coefficient and the regression coefficient or, in simple terms, the difference between how well the line fits the data and how steep the slope of the line is.
Using standard stepwise regression techniques (Draper and Smith, 1998), it was found that several of the predictor properties were highly correlated with the corrosion current. However, having fitted one of these properties as a single predictor, the model could not be improved by the addition of a second or further predictors. This phenomenon is due largely to the high correlations existing among the transport properties themselves. Nonetheless, a comparison of the single predictor models is instructive.
The t-ratio was used to assess the significance of the correlation between corrosion current and each transport property. Using the regression coefficients (or slopes) to compare the size of the effect of each predictor on corrosion current is complicated by the different units of measurement adopted for each predictor. This difficulty has been overcome by calculating the change in corrosion current predicted by each single predictor model over the range of samples tested. The validity of this method of comparison relies on the careful design of the experiment in selecting the range of values for each predictor to reflect the full range of normal site conditions.
It should be noted that, for each model used, a thorough residual analysis was conducted to check for the possibility of non-linearity or heteroscedasticity. A normal probability plot was used to test for normality of residuals. In the case of oxygen permeability, these diagnostic checks indicated that a logarithmic transformation of the predictor was necessary.
13.4.3 Results
The effects of the predictors and their t-ratios are given in Table 13.2 for the initial corrosion current and Table 13.3 for the 28 day corrosion current. The effects are shown in Figs 13.4 and 13.5 (note that the scales are different). In these figures, the predictors are labelled using the abbreviations from Table 13.2.
Table 13.2
Effect of predictors on initial corrosion current
| Property | Effect | t-ratio |
| SF concrete | ||
| Strain 18 | NS | |
| Cl conc. | 1.124 | 3.13 |
| Log K(O2) | NS | |
| Cube strength | 1.596 | −5.31 |
| Depth 18 | NS | |
| Depth 28 | NS | |
| Conductivity | 1.061 | 3.86 |
| Lime | 1.689 | 6.05 |
| Vapour | 0.798 | 2.39 |
| PC concrete | ||
| Strain 18 | NS | |
| Cl conc. | 0.611 | 2.92 |
| Log K(O2) | 0.456 | 2.28 |
| Cube strength | 0.584 | −2.64 |
| Depth 18 | NS | |
| Depth 28 | NS | |
| Conductivity | 0.57 | 3.38 |
| Lime | NS | |
| Vapour | NS | |
Note:
The 5 % critical t-value is 2.032.
The 1 % critical t-value is 2.728.
The 0.1 % critical t-value is 3.601.
NS = not significant.
Table 13.3
Effect of predictors on 28 day corrosion current
| Property | Effect | t-ratio |
| SF concrete | ||
| Strain 18 | 0.595 | 2.27 |
| Cl conc. | 0.550 | 2.22 |
| Log K(O2) | 0.803 | 3.98 |
| Cube strength | NS | |
| Depth 18 | NS | |
| Depth 28 | NS | |
| Conductivity | 0.641 | 3.51 |
| Lime | NS | |
| Vapour | 0.586 | 2.77 |
| PC concrete | ||
| Strain 18 | 4.303 | 5.17 |
| Cl conc. | 3.577 | 5.80 |
| Log K(O2) | 3.533 | 6.72 |
| Cube strength | 3.431 | −4.98 |
| Depth 18 | 2.921 | 3.02 |
| Depth 28 | 2.574 | 6.79 |
| Conductivity | 2.572 | 4.45 |
| Lime | 2.564 | 2.98 |
| Vapour | 1.806 | 2.30 |
Note:
The 5 % critical t-value is 2.032.
The 1 % critical t-value is 2.728.
The 0.1 % critical t-value is 3.601.
NS = not significant.
13.4.4 Discussion
The cube strength was the only predictor which had a negative coefficient, i.e. high strength indicated low corrosion as expected. The effect of oxygen transport as a predictor is not justified directly in this instance because the corrosion was shown to be anodically controlled. This was checked using equation (13.3). It may be seen from the right hand side of this that if ϕc0 and Ic0 remain constant, the rest potential will decrease linearly as the corrosion current increases. This was observed for this data (Cabrera and Claisse, 1995) indicating that the cathode conditions were the same for all samples. However, oxygen transport remains a good general measure of transport in the concrete.
The initial current
For the Portland cement (PC) mixes, five of the nine predictors were not significant. None of the measurements of carbonation (Strain 18, Depth 18 and Depth 28) or the vapour transport or the lime content were significant. The most significant predictor was the electrical conductivity because none of the transport properties will have been significant before exposure. The remaining significant predictors are chloride transport (Cl conc.), oxygen permeability (log K(O2)) and cube strength which are only significant because they measure the general ‘quality’ of the concrete. The effect of the four significant predictors on the corrosion current is very similar implying that changes in any of them would indicate the same change in corrosion current.
For the SF mixes, the lime content becomes the most significant predictor and also has the greatest effect. The mechanism of conduction of direct current discussed in Chapter 10 suggests that it is substantially controlled by the amount of lime (hydroxyl ions) present. The high significance of the lime content is therefore due to a combination of its effect on the electrical conductivity and its depletion as the pozzolanic reaction of the SF proceeds and the transport properties decrease. This high significance implies that the pozzolanic reaction is not depleting the lime sufficiently to affect the alkalinity of the steel because this would cause corrosion to increase as the lime content decreased giving a negative t-ratio. The high significance and effect of the cube strength (greater than all of the remaining transport properties) was unexpected.
The 28 day current
The PC mixes generally performed as expected with every predictor being significant. Having been insignificant for the initial current, the carbonation strain has become the second most significant predictor and the oxygen permeability the most significant. The conductivity remains significant but has been overtaken by many transport properties. Figure 13.5 shows the effects in decreasing order indicating that the carbonation strain has greatest effect followed by the chloride transport next. Because the exposure took place in chloride solution, the chloride transport would have been expected to be greatest, but all of these properties are highly correlated.
The SF mixes showed significantly lower changes in corrosion current because their corrosion currents were generally significantly lower. An important observation was that, in contrast to the result for the initial current, the cube strength was not significant as a predictor. This implies that producing high strength mixes with SF is not a route to durability of embedded steel in a chloride environment. The lime content was also not significant. The failure of the two measures of carbonation depth to work as predictors was caused by the very low (and often nil) depths observed.
13.5 Predictive models for corrosion
Equation (12.1) is used as the basis for a number of models that are used to predict chloride ingress into concrete and, from it, the durability of structures.
Software packages such as Life-365 (http://www.nrmca.org/research_engineering/Life365.htm) use equation (12.1) and take no account of ion–ion interactions. These packages are used to predict the life of structures and influence design decisions such as the depth of cover to the reinforcement of the w/c ratio of the mix. The package is set up so recommended values of the diffusion coefficient are given for different mixes, however, it would be possible for users to input their own values if experimental data was available.
In Chapter 12, the limitations of this approach were shown to be significant. These limitations are most apparent when different mixes are compared which have different concentrations of other ions which can carry current. SF is a good example of this because the strong pozzolanic reaction depletes the lime and thus the hydroxyl ions.
The first approach to overcoming this could be to use a different test. ‘Simple gravity’ diffusion tests are discussed in Chapter 12 and shown to be ineffective if the other ions are not modelled. A further test type is the Nordtest chloride migration test.
13.5.1 The Nordtest NT Build-492 test
This test, shown in Fig. 13.6, is similar to the ASTM C1202 test described in Chapter 10 in that a voltage is used to drive chlorides into the sample (NTBUILD, 1999). However, the results are obtained by cutting up the sample and measuring the chloride content at different depths at the end of the test. The results are then analysed using an integrated form of the Nernst–Planck equation (1.26). No account is taken of the ion–ion interactions.
Figures 13.7 and 13.8 show the effect of ion–ion interactions on this test. They may be seen to be very significant. The concentration is completely changed by the ion–ion interactions. Thus any diffusion coefficient obtained directly from equation (1.26) will be incorrect.
13.5.2 Predictions with the ASTM C1202 test
The ASTM C1202 test is not normally used to calculate a diffusion coefficient (although some authors have used equation 10.8). The result is normally simply given as charge passing. In some project specifications, a maximum charge passing of 1000 C is specified and the mix design is left to the contractor with no further checks for durability.
Figure 13.9 shows results for the mixes A and B described in Chapter 8 after 28 and 90 days of curing. The results from the gravity diffusion test are compared with those from the ASTM C1202 migration test. The pozzolanic mixes generally have coulomb values below 1000 and the CEM1 mixes above (the only SF mix above 1000 C was from 28 days of cold curing so the pozzolanic reaction would not have progressed). This data indicates that the ASTM C1202 test is not suitable for this purpose.
13.5.3 Discussion
For modelling concrete durability, it has been noted that neither the simple diffusion test nor the durability models take account of ion–ion interactions. It may also be seen that the simple diffusion test has a good resemblance to the geometry of an exposed concrete surface on site. It may therefore be indicated that results from the test may be used in the model, subject to concerns about changing conditions which may affect adsorption or ionic concentrations. It is indicated that the use of coefficients from electrical tests in these durability models should only be attempted if numerical simulations are used to correct for the effect of the ion–ion interactions.
Any test can be used for site quality control purposes provided it is only used for comparative purposes on similar mixes. Thus the ASTM C1202 test could be used very effectively for this purpose provided initial tests were carried out on samples which were known to be of adequate quality. Provided the contractor did not start adding more pozzolan in the mix, any sample giving results as low as the initial tests could confidently be confirmed to be satisfactory.
13.6 Conclusions
• The corrosion of steel in concrete is controlled by the transport processes, but the relationship is complex.
• The electrical conductivity and the chloride transport were the only two predictors of corrosion which were significant for all situations and the conductivity was more significant than the chloride transport in three out of four.
• All measurements of diffusion in concrete, with or without applied voltages, are significantly affected by ion–ion interactions.
• For the comparison of mixes with different cementitious materials in them, a simple diffusion test should be used unless computer modelling is used to correct the results of electrical tests.
• The electrical tests are suitable for quality control purposes.
• For modelling the life of structures, a diffusion coefficient which includes some ‘adjustment’ for ion–ion interactions (such as that obtained by applying Fick’s law to a simple diffusion test) could be used (if the model itself also uses Fick’s law without corrections for ion–ion interactions).