Table VII also contains the values of Au, k, and t0 determined via the nonevaporable water content measurements at 15º and 35ºC. As would be expected, the rate constant (k) is a strong function of temperature. In addition, the induction period (t0) decreases slightly with increasing temperature, as does the value of the asymptotic nonevaporable water content (Au). Geiker 29 has noted a similar trend for the values of Au, quoting values of 0.206, 0.201, and 0.198 g of H2O/(g of cement) for curing temperatures of 20º, 35º, and 50ºC, respectively, for a rapid hardening portland cement with w/c = 0.45, based on the data of Munkholt.61 Perhaps the simplest method for relating model results calibrated at 25ºC to other temperatures is through the use of a maturity-type approach51, 62 (see Panel D). Table IX summarizes the values determined, using this approach, for the apparent activation energies for the rate of hydration for Cements 115 and 116 for the three w/c ratios investigated in this study. The values, all in the range of 35-42 kJ/mol, are in good agreement with those previously determined for cementitious systems, as summarized by Tank and Carino.44
|Table IX. Apparent Activation
Energies for Hydration of Cements 115 and
116 as Determined by the Maturity-type
(kJ / mol)*
|*Numbers in parentheses indicate approximate standard deviation provide by DATAPLOT 53|
Using the average value of the activation energies given in Table IX, 38.2 kJ/mol, multiplicative factors of 0.585 and 1.65 would be necessary to convert the curing times at 15º and 35ºC to equivalent times at 25ºC, respectively. Using these two values, Fig. 16 provides plots of the degree of hydration, estimated via the nonevaporable water content, versus time for the two cements and three w/c ratios. In every case, using the equivalent time concept collapses the three data sets onto a single master curve. Although some dispersion is seen at longer times, in general, the three data sets asymptotically approach about the same value for degree of hydration, for a fixed cement and w/c ratio. Based on a simple application of the gel-space ratio concept described previously, one would expect that these systems might also have the same ultimate strength values. This, however, is in contrast to measured compressive strength values for concretes with w/c 0.45, 62, 63 where the ultimate strength is significantly higher the lower the curing temperature (e.g., the ultimate strength for a concrete cured at 10ºC may be 180% of that for an equivalent concrete cured at 40ºC). The most likely explanation for this discrepancy is that the intrinsic strength of the cement hydrates is a function of curing temperature. This would change the value of A, in Eq. (9) and alter the values of the coefficients used in Eq. (8). Because Geiker 29 has noted that the measured chemical shrinkage is significantly less for samples cured at elevated temperatures, it would seem likely that the C-S-H gel formed at higher temperatures is incorporating less water into its gel structure, in turn implying a denser gel. This increased density of the C-S-H gel also would be consistent with the increased and coarser capillary porosity measured on samples cured at higher temperatures. 64, 65 In this case, to truly model the effects of temperature on hydration and microstructure, the stoichiometry, molar volume, and density of the C-S-H phase should be a function of curing temperature. However, if one's main interest is in predicting degree of hydration, the maturity-type approach coupled with the current version of the NIST cement hydration model appears to be adequate, based on the results in Figs. 12 and 16.
Fig. 16. Superposition of degree of hydration results at three temperatures for CCRL Cements 115 and 116