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 *t*_{0}, 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 *A*_{u}
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 *A*_{u} 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 *t*_{0} (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 ConvertingCycles to Time for Cements 115 and 116 |
||
---|---|---|

Cement | w/c |
B |

115 | 0.30 | 0.0014 |

115 | 0.40 | 0.0023 |

115 | 0.45 | 0.0020 |

116 | 0.30 | 0.0013 |

116 | 0.40 | 0.0016 |

116 | 0.45 | 0.0016 |

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 *t*_{0, }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.