## 3 Results
### The Parameter Analysis for Each Cementitious Material in CCSDOT Model
#### 3.2.3 Limestone Flour  
\(ss_{LF}\), \(\lambda_{LF}\) and \(i_{LF}\) are shown in Figures 5-7, respectively. In Figure 5, most of \(ss_{LF}\) are between \(-0.437\) and \(-0.761\) while the median of \(ss_{LF}\) is \(-0.676\). Limestone flour is a kind of inert material [36]; therefore, there is almost no chemical action [34] to concrete. In early days, limestone flour even has a negative effect on concrete's compressive strength compared to cement. Therefore, the \(ss_{LF}\) are smaller than 0. In Figure 6, the \(\lambda_{LF}\) are between \(0.118\) and \(0.381\) generally; the median is \(0.194\). Limestone flour has a polygonal body with an irregular shape whilst its morphology is similar to cement. As a result, it can improve the gradation of fine powder when mixed into concrete. Through the micro-aggregate effect and filling effect of limestone flour, the mechanical bite force between the mortar and aggregate is increased. Thus, physical action of the limestone flour at later days exits. The \(\lambda_{LF}\) are greater than 0. In addition, most of \(i_{SL}\) are between \(1.516\) and \(1.847\), while the median of \(i_{SL}\) is \(1.598\).  
Step 2: keep the total amount of cementitious material unchanged, and make the fly ash content in concrete gradually increase from 0% to 80% by weight with 1% interval; then we get 81 concrete mix proportions.  
Step 3: substitute the 81 mix proportions into the calibrated CCSDOT model, then we obtain 81 corresponding curve of concrete compressive strength development over time in Figure 9.  
Step 4: according to the concrete age and compressive strength in the design requirements, maximum dosage of fly ash can be quickly obtained from Figure 9 by using the abscissa and ordinate.  
Figure 10 indicates the change characteristic of the compressive strength of concrete with the increase of fly ash content. The concrete compressive strength decreases as the fly ash dosage increases throughout all the concrete's age. The black, red, blue, and green curves denote the concrete at 7, 28, 90, and 180 days respectively. In order to better clarify the relationship among fly ash content, concrete compressive strength, and concrete's age, the relative compressive strength of the concrete is introduced to show the influence of fly ash content on the concrete's compressive strength at different ages. Figure 11 shows the relationship between the content of fly ash and the relative compressive strength of the concrete. Relative compressive strength of concrete at a certain age decreases as the increasing of fly ash content, and relative compressive strength of concrete with a certain content of fly ash deceases as the increasing of concrete's age. Table 11 shows the compressive strength of concrete with 0%, 40%, and 80% content of fly ash by weight at 7 days, 28 days, 90 days, and 180 days, respectively. As you can see, fly ash content has less influence on the concrete's compressive strength as the age increases.  
Figure 9: The relationship between the concrete’s age and compressive strength with 1% interval of the fly ash’s dosage. Black cross marks are tested value.  
Figure 11: The relationship between the content of fly ash and the relative compressive strength of concrete.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Concrete Age (day)**} & \multicolumn{3}{c}{**Compressive Strength of Concrete (MPa)**} \\ \cline{2-4}  & **0\% Fly Ash** & **40\% Fly Ash** & **80\% Fly Ash** \\ \hline
7 & 9.89 & 6.34 & 1.19 \\
28 & 29.81 & 23.81 & 12.57 \\
90 & 46.59 & 38.52 & 22.15 \\
180 & 56.55 & 47.25 & 27.84 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Compressive strength of concrete with 0%, 40%, and 80% content of fly ash.  
Figure 10: The relationship between fly ash content and compressive strength of concrete day-by-day. Black cross marks are tested value.