To fit the model results to those measured experimentally, a conversion between cycles and time is necessary. The simplest conversion would be to use a linear proportionality (time = B x cycles). However, it has been pointed out previously to the author that, if one assigns unit real time to each iteration of the NIST cement hydration model, linear kinetics are generated that closely follow Knudsen's linear dispersion model.57 But, because experimental observations largely indicate parabolic hydration kinetics, a better match between model kinetics and experiment has been sought by investigating an alternative iteration-time mapping, namely
|time(h) = t 0+ B x (cycles) 2||(7)|
with the t0, term (from Table VII) included because the current version of the cement hydration model covers only the post-induction period. In this way, the linear kinetics obeyed by the model can be adapted to the parabolic kinetics exhibited by the real cements.
To calibrate the model to the experimental results based on the nonevaporable water content data, the model results for degree of hydration have been regressed in Eq. (6) using the earlier deduced parameters for Au and k, and a subset of the model degree-of-hydration data. This subset has been generated by selecting single data points at ~0.05 degree-of-hydration intervals for values of degree of hydration between 0.10 and the amount of hydration achieved experimentally at 90 d. In this way, the regression being applied to the model is being weighted in approximately the same manner as that which has been applied to the experimental results. This step is deemed necessary because the model degree of hydration values are not evenly distributed with number of cycles (i.e., more hydration occurs during the early cycles than during the later ones). The previously determined value of Au has been converted to a degree of hydration, via normalization by the value for the nonevaporable water content at complete hydration (0.226 or 0.235). The coefficients determined for B as a function of cement and w/c ratio are summarized in Table VIII. Interestingly, the values for B are relatively constant, suggesting that a constant value of B (such as the average B value of 0.0017) can serve to model all of the results for the two cements and three w/c ratios. From the variability in the results in Table VII, an average value of t0 (namely 6.7 h) also may suffice for these two particular cements at 25ºC. This value is slightly larger than the final times of set measured for the two cements using the Vicat and Gillmore needle techniques, which are both on the order of 5 h. 20
|Table VIII. Parameter for Converting
Cycles to Time for Cements 115 and 116
Once a value(s) of B has been determined, plots comparing model and experimental results can be generated. Figures 12, 13, and 14 provide example fits of the model to the experimental data for Cement 115 with w/c = 0.40. In these figures, the solid lines indicate the model data obtained using the specific values of t0, and B for w/c = 0.40 for Cement 115, as given in Tables VII and VIII, and the dotted lines indicate the results that would be obtained using single average values for these parameters regardless of w/c ratio and cement identification. Figures 12, 13 and 14 show that the agreement between the solid lines and the experimental data is, in general, excellent. For the other w/c ratios and for Cement 116, the quality of the fits is similar to that exhibited in Figs. 12, 13, and 14. For the dotted lines, the agreement is similar, suggesting that, for these two cements, a single relationship can be used to convert model cycles into real time. This suggests that, by capturing the particle- size distribution and phase distributions of the cements, much of the hydration kinetics behavior is implicitly included in the hydration model; i.e., the initial cement particle microstructure has a large influence on the postinduction period kinetics of cement hydration. Thus, a calibration performed for one cement at one w/c ratio can be used to predict the hydration behavior of other cements, of reasonably similar phase composition, at a variety of w/c ratios.
Fig. 12. Measured and model degree of hydration versus time for Cement 115 with w/c = 0.40.
Fig. 13. Measured and model chemical shrinkage versus time for Cement 115 with w/c = 0.40.
Fig. 14. Measured and model heat release versus time for Cement 115 with w/c = 0.40.