*4.3. Calculation of Reaction Rate Constant (kT) and Apparent Activation Energy (Ea)*

The relationship between age and compressive strength was analyzed, and *kT* was obtained according to the GGBFS replacement ratio. Figure 4 shows the reciprocal of compressive strength versus reciprocal age. By dividing the y-intercept of the linear regression line by the slope, we can derive the *kT* that takes the curing temperature and the replacement ratio as variables. Figure 5 shows *kT* according to the GGBFS replacement ratio at each curing temperature. As the curing temperature increased, the *kT* increased in the form of an exponential function and showed a high correlation between 0.87 and 0.99. In addition, the lower the GGBFS replacement ratio at the same curing temperature, the higher the *kT*. The *kT* of 50% GGBFS mortar is decreased by 75% and 70% at 5 ◦C and 35 ◦C curing temperature, respectively compared to OPC. In addition, the reaction rate constant of OPC and 50% GGBFS mortar is decreased by 76% and 81% at 5 ◦C compared to 35 ◦C curing temperature, respectively. Therefore, the curing temperature and GGBFS replacement ratio have a complex effect on the *kT*.

**Figure 4.** Regression analysis results for calculating *kT* (**a**) 0%, (**b**) 10%, (**c**) 30%, (**d**) 50%.

**Figure 5.** The effect of temperature on the rate constant with GGBFS replacement ratio.

By taking the natural logarithm of the calculated *kT* and plotting the reciprocal of the curing temperature (K), we can represent the Arrhenius plot, as shown in Figure 6. The gradient of the linear regression line of each GGBFS replacement ratio represents *Ea*/*R*, and the y-intercept represents the value of *ln*(*A*). As the GGBFS replacement rate increases, the gradients of the linear regression line decreases to a negative value.

Figure 7 shows the *Ea* results of GGBFS replacement ratio. As the GGBFS replacement ratio increases, the *Ea* increases linearly, which considered as the result of an increase in the minimum energy for the chemical reaction of cement, GGBFS and water. For OPC mortar, *Ea* is estimated to be 33.475 kJ/mol, which is very similar to the proposed value of Freisleben-Hansen and Pederson, i.e., 33.5 kJ/mol [13]. Wirkin et al. have found that superplasticizer has a little role on the hydration kinetics of cement and the difference in *Ea*, with or without the superplasticizer, is insignificant, i.e., 3 kJ/mol [44]. In the present study, the *Ea* value of 10%, 30% and 50% GGBFS is found to be 37.325 kJ/mol, 41.958 kJ/mol and 45.541 kJ/mol, respectively.

**Figure 6.** Arrhenius plot of ASTM C 1074 for calculating *Ea.*

**Figure 7.** Apparent activation energy according to the GGBFS replacement ratio.

#### *4.4. Prediction of Compressive Strength of Concrete with GGBFS*

#### 4.4.1. Compressive Strength of Concretes

This study measured the compressive strength of concrete with GGBFS at the age of 3, 7, 14, and 28 days and used the average of compressive strength of three specimens as a result. The results of compressive strength with varying curing temperature and GGBFS replacement ratio are shown in Figure 8. At higher curing temperatures, the compressive strength increased, and as the GGBFS replacement ratio increased, the compressive strength decreased. In addition, the difference in compressive strength with the change of curing temperature is the largest at three days of age. As the GGBFS replacement ratio increased, the difference in compressive strength, due to curing temperature increased. Especially, 28 days of age, the difference in compressive strength of OPC concrete at curing temperature of 5 ◦C and 35 ◦C was about 2.6 MPa, and the difference in compressive strength of 50% GGBFS is about 7.9 MPa. At curing temperatures of 5 ◦C, the compressive strengths of OPC, 10%, 30% and 50% GGBGS at three days were 12.1 MPa, 8.6 MPa, 4.3 MPa and 2.4 MPa, respectively. By increasing the GGBFS replacement ratio at low curing temperature causes delayed development of compressive strength in early age. Therefore, GGBFS concretes have different compressive strengths than OPC concrete. Thus, accurate prediction is necessary.

**Figure 8.** Compressive strength of concrete with curing temperature and GGBFS replacement ratio (**a**) 0%, (**b**) 10%, (**c**) 30%, (**d**) 50%.
