Table VII also contains
the values of *A*_{u}, *k*,
and *t*_{0} 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 (*t*_{0}) decreases slightly with
increasing temperature, as does the value of the asymptotic nonevaporable
water content (*A*_{u}).
Geiker^{ 29}
has noted a similar trend for the values of *A*_{u}, quoting values of 0.206, 0.201, and 0.198 g of
H_{2}O/(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
approach^{51,
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 ActivationEnergies for Hydration of Cements 115 and 116 as Determined by the Maturity-type Approach |
||
---|---|---|

Cement | w/c |
Activation energy (kJ / mol)* |

115 | 0.30 | 39.3 (0.6) |

115 | 0.40 | 41.3 (1.2) |

115 | 0.45 | 36.9 (6.0) |

116 | 0.30 | 36.5 (11) |

116 | 0.40 | 40.0 (3.8) |

116 | 0.45 | 35.3 (3.2) |

*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