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 time51 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 = k0 exp (- Ea/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 Ea 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, Ea 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 (Ti ) an equivalent time (te ) can be calculated relative to a reference temperature (Tr , 25ºC in this study), as
where kT , is the rate constant at the experimental temperature of interest, kr , 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.