The maturity method has been developed to provide a quantitative technique
for predicting the in-place compressive strength development of a concrete,
based on its thermal history.^{
62} Because strength is strongly linked to the amount of
cement that has reacted (degree of hydration), this approach should also be
applicable to predicting the effects of temperature on hydration kinetics. In
fact, the expressions commonly used in the maturity method to relate strength
to time^{51}
are equivalent to the dispersion models of Knudsen,^{
52} which are being used in the
present study to relate degree of hydration to time. Basically, the maturity
method accounts for the time-temperature history of the curing of a concrete
by determining a relationship between temperature and a rate constant,
typically a rate constant for compressive strength development, but, in our
case, one for degree of hydration development (*k* in Table
VII).

Typically, an Arrhenius function of the form

k =
k_{0} exp (- E_{a}/RT ) | (10) |

is fitted to the values of the rate constant *k* versus temperature,
such as those provided is Table VII.
In Eq. (10), *T* is the absolute
temperature (in kelvin), *R* the universal gas constant (8.314
J/(mod·K)), and *E*_{a} an
*apparent* activation energy (typically in kJ/mol). Because the
different mineral phases of a cement may react at different rates,
implying a nonhomogeneous system, *E*_{a} is not a true activation energy but, rather, provides an apparent
value.^{51}
Based on Eq. (10) a plot of In *k* 1/*T* should give a straight line whose slope is proportional to *E*_{
a}. Although alternatives to the Arrhenius
equation, such as a simple exponential function (e.g., *k* = *A
*_{0} exp (*BT*), *T* in ºC), have been explored previously,^{
51} for this
study, the Arrhenius equation generally was found to provide the better fit
(smaller residual standard deviation) to the data. Once *k* has
been determined as a function of temperature, then, at any
temperature of interest (T_{i }) an
equivalent time
(t_{e }) can be calculated relative to a
reference temperature
(*T*_{r }, 25ºC in this study), as

(11) |

where *k*_{T }, is the rate
constant at the experimental
temperature of interest, k_{r }, the rate
constant at the reference temperature, and *t *the elapsed time at the
experimental temperature. In this way, time values at which degree of
hydration has been measured at any temperature can be converted to equivalent
times at 25ºC, so that data obtained at various temperatures can be
plotted on a single equivalent time axis, in hopes of obtaining a
single curve for degree of hydration versus equivalent
time.