*2.2. Reaction Rate Constant(kT) and Apparent Activation Energy (Ea)*

The cement reacts with water at an early age resulting hydration reaction. Due to the hydration of cement paste in concrete, it develops strength. The hydration rate is governed by the reaction rate constant of the point when the cement paste and water react [24,28]. The hydration degree of Portland cement can be derived by the weight ratio of reaction products. The weight ratio of reaction products can be determined by non-hydrated cement using an electron microscope or X-ray diffraction analysis [29–32]. Also, the degree of hydration can be measured by the amount of water, as well as heat generation, and the compressive strength in an indirect way. The most common indirect hydration measurement method used in Portland cement is the micro-hydration method using conduction calorimeter. It measures the amount of hydration heat generated at the beginning when hydration of cement starts with time and represents the ratio of calorific value of final hydration per weight of cement [33]. This method accurately shows the degree of hydration at the beginning of cement hydration, but cannot change the degree of hydration, due to change in curing process [27]. The reaction rate constant is the indicator of the initial gradient for the degree of hydration. There are many factors which affect the reaction rate constant. However, it is difficult to quantitatively predict the effect of temperature on the reaction rate constant. Therefore, the reaction rate constant can be represented by the function of curing temperature if other conditions are identical. It is known that the reaction rate constant is influenced by the types of cement, curing temperature, W/C (%), admixture, and humidity conditions etc. [9,34–37]. Thus, activation energy (*Ea*) can help to calculate the reaction

rate constant where minimum energy is required to occur the reaction. It has been reported that *Ea* can vary owing to the nature of Portland cement, which has different hydration reaction patterns with the setting process, curing period, and cementitious components [38]. Some researchers have reported that *Ea* is approximately 33.5 to 47.0 kJ/mol at early-age, and approximately 10 to 30 kJ/mol at long-term age [39–49]. Freisleben-Hansen and Pederson (FHP) [13] proposed an equation (Equation (7)) to estimate *Ea* of OPC concrete as a function of curing temperature.

$$E\_4 = 33.5 + 1.47(20 - T\_a) \text{kJ/mol} (T\_a < 20 \, ^\circ \text{C}),\tag{7a}$$

$$E\_a = 33.5 \text{kJ/mol} (T\_a \ge 20 \text{ }^\circ \text{C}), \tag{7b}$$

where *Ea* is apparent activation energy by Freisleben-Hansen and Pedersen with temperature parameter, *Ta* is the average curing temperature of concrete during a time interval.

However, Carino pointed out that *Ea* can be determined by the composition, powder level, type, amount, and admixture of the cement [25,26], and other researchers argue that the *Ea* is changed by W/C ratio.

The hydration reaction of Portland cement can be formulated with *Ea*. Therefore, ASTM C 1074 [21] has suggested the method to determine the *Ea*. The procedure for determining the *Ea* and the compressive strength prediction procedure, according to ASTM C 1074 is shown in Figure 1.

**Figure 1.** Calculation of *Ea* and estimation of compressive strength of concrete according to ASTM C 1074.

The final setting time of the mortar cured at three different temperatures is measured. The compressive strength of mortar is measured at 2, 4, 8, 16, 32 and 64 times as the final setting time. By plotting the reciprocal of the age(*x*-axis) versus the compressive strength (*y*-axis), the y-intercept of the linear regression line can be obtained from the regression analysis. *Ea* can be calculated by plotting the reciprocal of the curing temperature(*x*-axis) versus the reciprocal of *lnkT* (*y*-axis) and dividing the

gradient of the linear regression line obtained from the regression analysis. The equivalent age can be calculated by *Ea* of GGBFS concrete from Equation (5), and the compressive strength development is analyzed by the calculated equivalent age and *kT* from Equation (6).

#### **3. Experimental Program**
