## 3 Results  
### Performance of the CCSDOT Model  
The 239 groups of concrete mix proportions are adopted in this study. Based on the modified SQP method, we substitute the proportions and the tested concrete compressive strength into the CCSDOT model, and obtain the fitted value. An intuitive comparison between the fitted value and the tested value of concrete compressive strength is shown in Figure 3, including concrete incorporated with fly ash (_FA_), concrete mixed with fly ash and limestone flour (_FA + LF_), concrete incorporated with fly ash and slag (_FA + SL_) and concrete mixed with limestone flour (_LF_). It is demonstrated that the fitted value is very close to the tested value graphically. The correlation coefficient (R\({}^{2}\)) for 7-day, 28-day, 90-day, and 180-day compressive strength of concrete incorporated with a different kind of supplementary cementitious materials are listed in Table 7. Most of the R\({}^{2}\) are greater than 0.98. \begin{table}
\begin{tabular}{c c} \hline
**Abbreviation** & **Implication** \\ \hline _SL_ & Slag \\ \hline _FA_ & Fly ash \\ \hline _LF_ & Limestone flour \\ \hline \(C\) & Cement \\ \hline _FA + SL_ & Fly ash and slag \\ \hline _FA + LF_ & Fly ash and limestone flour \\ \hline _ss\({}_{FA}\) (_FA + SL_) & the 28-day compressive strength contribution coefficient of fly ash in the concrete mixed with fly ash and slag \\ \hline _ss\({}_{FA}\) (_FA_) & the 28-day compressive strength contribution coefficient of fly ash in the concrete mixed with fly ash \\ \hline _ss\({}_{FA}\) (_FA_ + _LF_) & the 28-day compressive strength contribution coefficient of fly ash in the concrete mixed with fly ash and limestone flour \\ \hline _x\({}_{FA}\) (_FA + SL_) & the factor in later periods of fly ash in concrete mixed with fly ash and slag \\ \hline _x\({}_{FA}\) (_FA_) & the factor in later periods of fly ash in concrete mixed with fly ash and limestone flour \\ \hline _x\({}_{FA}\) (_FA + _LF_) & the factor in later periods of fly ash in concrete mixed with fly ash and limestone flour \\ \hline \end{tabular}
\end{table} 
Table 6: Abbreviation in the rest of this study. Figure 3: Relationship between tested compressive strength and fitted concrete compressive strength. Moreover, we use \(RMSRE_{j}\) to evaluate the error between the fitted and tested compressive strength of concrete as presented in Figure 4. The results are analyzed in four different scenarios, including concrete with fly ash, with fly ash and limestone flour, with fly ash and slag, and with limestone flour. \(RMSRE\) is generally small and confined between 0 and 10%. The \(RMSRE\) of concrete mixed with fly ash, and the \(RMSRE\) of concrete incorporated with fly ash and slag, are relatively small due to the sufficient data. In addition, the 25 th percentile, median and 75 th percentile of \(RMSRE\) of the four kinds of concrete are shown in Table 8. The \(MRMSRE\) for four scenarios are 3.9374%, 5.4667%. 4.0506%, and 7.4667% respectively. The \(MRMSRE\) of concrete with fly ash and that with fly ash and slag are acceptable in practical engineering, which requires no more than 5%. Since the quantity of concrete mix proportions are insufficient, the \(MRMSRE\) of concrete with fly ash and limestone flour and that with limestone flour only are slightly great. Considering each group of concrete mix proportion contain two or more similar mix proportions, the \(MRMSRE\) are still acceptable. In conclusion, the proposed model could fit the compressive strength of all four kinds of concrete fairly well, and can be used to deduce generic law of the influence of slag, fly ash, and limestone flour on concrete compressive strength. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Concrete Age** & _FA_ & _FA + LF_ & _FA + SL_ & _LF_ \\ \hline
7-day & 0.9946 & 0.9793 & 0.9946 & 0.9825 \\
28-day & 0.9928 & 0.9873 & 0.9906 & 0.9802 \\
90-day & 0.9928 & 0.9902 & 0.9802 & 0.9891 \\
180-day & 0.9914 & 0.9837 & 0.9670 & 0.9980 \\ \hline \hline \end{tabular}
\end{table}