As an example of the use of the CIKS, let us compare the performance, with respect to chloride resistance, of a conventional (24.1 MPa [3500 psi] 28 day compressive strength) and a high-performance (strength- 48.3 MPa [7000 psi]) concrete. We will specify a non-air entrained concrete with a low slump of 50 mm (2 in.). For the high-strength concrete, the maximum aggregate size will be 25 mm (1 in.) and no high-range water-reducing admixture will be employed. The other parameters will be specified as shown in the input forms in Figs. 2-4. The results in Table 1 contrast the trial mixture proportions, the predicted chloride ion diffusion coefficients, and the predicted service lives for the two mixtures. The confidence limits for D for the conventional concrete are seen to be much wider than those for the high-performance concrete, due to the fact that the confidence limits naturally tend to widen away from the mean parameter values used in the computer experiment (w/c=0.45, volume of aggregate=67.5%, and degree of hydration=0.6).
For the prediction of service life, in addition to the estimated diffusivity coefficients, the other values, as shown in the form in Fig. 7, were taken from Example 1 (representative of a bridge deck in Kansas) in the report by Weyers et al. . The high-strength concrete, mainly due to its lower porosity, is seen to offer a service life that is over seven times as long as the conventional concrete. In this case, by doubling the compressive strength, we have achieved even a greater proportional increase in estimated service life.
|Table 1: Mixture proportions and properties for ordinary and high-strength concrete|
|28-day compressive strength MPa (psi)||24.1 (3500)||48.3 (7000)|
|Air content||1 percent||1.5 percent|
|Cement [kg/m3 (lb/yd3)]||272 (459)||597 (1006)|
|Water [kg/m3 (lb/yd3)]||167 (282)||185 (312)|
|Fine aggregate [kg/m3 (lb/yd3)]||874 (1473)||470 (792)|
|Coarse aggregate [kg/m3 (lb/yd3)]||1172 (1975)||1201 (2024)|
|D [10-12 m 2/s (in.2/yr)]||7.0 (0.34)||0.9 (0.044)|
|90 percent confidence limits for D
[10-12 m2/s (in.2/yr]
|[0.8, 60.0] (0.04, 2.9)||[0.6, 1.4] (0.03, 0.07)|
|Estimated service life||4 years||30 years|
Figure 7: HTML input
form for predicting service life of concrete exposed
to chloride ions based on analysis using Fick's second law.
Figure 7: HTML input form for predicting service life of concrete exposed to chloride ions based on analysis using Fick's second law.
For the ordinary strength mixture, the estimated chloride ion diffusivity, along with the mixture proportions, was input into the form for predicting the chloride ingress profile. An exposure consisting of 120 days at a concentration of 4 mol/L followed by 240 days at a concentration of 0.1 mol/L was selected, with a total exposure time of 7200 days. This is intended to model a four-month winter period during which de-icing salts are applied, followed by an eight-month period of relatively low external chloride ion concentrations. The parameters for chloride binding were based on those given in the paper by Sergi et al. , with C3A and C4AF mass fractions of 4% and 8%, respectively. The diffusivity coefficient for the top 5 mm of the concrete was selected to be double that of the value for the bulk concrete given in Table 1, based on the lower volume fraction of aggregates generally present in the surface layer. The resultant predicted profile after the 7200 days of exposure is given in Fig. 8. Due to the reactions with the aluminates and the binding of chlorides, the total chloride concentration is much higher than the free chloride levels. In this case, if the reinforcement were located at a depth of 50 mm, substantial levels of free chloride (on the order of 0.5 mol/L) would be present at the reinforcement depth after 7200 days of exposure, consistent with the projected short service life given in Table 1 for a constant exposure condition.
Figure 8: Example results for predicted chloride ion (free and total) profiles for a conventional 24 MPa (3500 psi) concrete.