## 4 Discussion  
### Optimization of the RPC Mix Design Component  
Minitab software was used to perform RSM analysis to identify the combined effect of the WB and SF content change on the compressive strength of RPC for each curing period. As shown in Figure 13, both the SF content and the WB influence the compressive strength of RPC. Contour plots clearly present that the strength response surface possesses a dark green color area, and the light green colored area and grey colored area indicate high strength and low strength, respectively. For  
Figure 12: Effect of the WB on drying shrinkage of RPC: (**a**) one-day air curing; (**b**) seven-day moist curing.  
instance, as shown in Table 2, the mixture 0.22 WB-20 SF with coded values of WB (0) and SF (0) is located in the darkest green area in the 7-day contour plot. The area under this intersection represents the compressive strength value of 84.5 MPa, which indicates the highest compressive strength. On the other hand, the mixture 0.22 WB-15 SF with coded values of WB (0) and SF (\(-1.4142\)) has a very light green color, which indicates the lowest compressive strength. This trend is the same in the 28-day and 56-day contour plots.  
Figure 13: Contour plots for combined effect of WB and SF (%) on compressive strength: (**a**) 7-day plot; (**b**) 28-day plot; (**c**) 56-day plot.  
Minitab software was also used to perform quadratic regression analysis for the compressive strength of RPC. Equations 6-8 indicate the modeling equations of the effect of the WB and SF on 7-day, 28-day, and 56-day compressive strengths. The accuracy of the model was evaluated based on the R\({}^{2}\) values for each age. Figure 14 shows the regression analysis results. As shown in Figure 14, the R\({}^{2}\) values for the 7-day, 28-day, and 56-day compressive strengths are 89.81%, 63.52%, and 91.66%, respectively. The variation of R\({}^{2}\) values at different ages may be associated with the pozzolanic reaction of the SF. While the hydration of cement mainly dominates the early age strength development of RPC, the pozzolanic reaction, which reacts with calcium hydroxide (CH) to form C-S-H, fully charges the strength development at 56 days. This cement hydration and pozzolanic reaction respond to high R\({}^{2}\) values at both ages (7 days and 56 days). The relatively low R\({}^{2}\) value at 28 days may be attributed to the transition period of the ongoing pozzolanic reaction. It should be noted that all of the RPC mixtures that are used for RSM analysis were cured at a normal temperature (23 \(\pm\) 2 \({}^{\circ}\)C), which provide a relatively slow pozzolanic reaction.  
\[f_{c\ 7-day}=84.52-2.03 WB+4.92 SF-8.42 WB^{2}-9.36 SF^{2}-6.10 WB\times SF \tag{6}\]  
\[f_{c\ 28-day}=83.77-2.04 WB+0.68 SF-5.90 WB^{2}-4.62 SF^{2}-1.33 WB\times SF \tag{7}\]  
\[f_{c56-day}=86.10-1.28 WB+0.36 SF-1.71 WB^{2}-5.65 SF^{2}+7.428 WB\times SF \tag{8}\]  
Based on the RSM modeling, the coded values of WB and SF that are required to achieve the highest compressive strength at the age of 7 days, 28 days, and 56 days were determined to be (\(-\)0.2428, 0.3286), (\(-\)0.1857, 0.1), and (\(-\)1.4142, \(-\)0.9), respectively. These values respond (0.213, 21.16), (0.215, 20.35), and (0.180, 16.81) at the ages of 7 days, 28 days, and 56 days, respectively. While the first term refers to the WB, the second term indicates the SF content. Furthermore, the coordination of the WB and SF resulting in the highest strength (84.91 MPa) for the combined ages is (\(-\)0.2428, 0) which indicates that the WB = 0.213 and SF = 20.0%. This combination is similar to the tested mixture design of the WB = 0.22 and SF = 20%, having an average strength of 84.80 MPa.