# Experiment and Analytical Model for Pore Structure of Early-Age Composite Cement Pastes by LF-NMR
## 3 Results and Discussion
### Analytical Pore Structure Model
#### 3.3.4 Optimized Pore Structure Model  
Building upon the S. and M. model, the Weibull distribution, and the bimodal characteristic of the PSD of cement pastes, a bimodal model is proposed as follows:  
\[p(d)=A\Big{(}(1-\exp(-Bd^{C}))+\exp(E(d-G)^{F})\Big{)} \tag{6}\]  
where \(p(d)\) is the cumulative of pore volumes with diameters greater than \(d\); and \(A\), \(B\), \(C\), \(D\), \(E\), \(F\), and \(G\) are parameters affected by w/c, the dosage of fly ash, slag, and silica fume.  
The comparisons between the experimental data and the predicted results of the optimized model are presented in Figures 12-15. The model performance metrics are provided in Table 7. Both the predicted values and the experimental data exhibit an inverse sigmoid shape, with the cumulative volume probability decreasing as the pore size increases. The experimental data and predicted results of the optimized model are generally in agreement, with only minor discrepancies. It is observed that as the w/c ratio increases, the fitting curve shifts to the right, indicating that the proportion of larger pores rises with an increasing w/c ratio. Additionally, as the age of the samples progresses, the gap between the predicted results and the experimental data gradually narrows. For small pores, the cumulative volume probability increases with higher contents of fly ash, slag, and silica fume, while for larger pores, the total volume probability decreases with an increase in fly ash and slag content. This suggests that as the content of these admixtures increases, the proportion of smaller pores also increases. Furthermore, as the age increases, the impact of the admixtures becomes more pronounced.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample** & **Age (Days)** & \(B\) & \(C\) & **Correlation** & **Standard Error** \\ \hline \multirow{4}{*}{WC40} & 3 & 15.1829 & \(-\)1.0000 & 0.9991 & 0.0183 \\  & 7 & 15.5102 & \(-\)1.0288 & 0.9992 & 0.0164 \\  & 14 & 15.1023 & \(-\)1.0219 & 0.9992 & 0.0174 \\  & 28 & 15.9384 & \(-\)1.0671 & 0.9992 & 0.0170 \\ \hline \multirow{4}{*}{FA30} & 3 & 12,072.4900 & \(-\)2.7557 & 0.9992 & 0.0176 \\  & 7 & 11,392.3500 & \(-\)2.9982 & 0.9991 & 0.0192 \\  & 14 & 4480.3220 & \(-\)2.7742 & 0.9987 & 0.0224 \\  & 28 & 58.7800 & \(-\)1.9292 & 0.9979 & 0.0258 \\ \hline \multirow{4}{*}{SL30} & 3 & 360.1463 & \(-\)1.8819 & 0.9997 & 0.0111 \\  & 7 & 157.6100 & \(-\)2.0545 & 0.9992 & 0.0170 \\ \cline{1-1}  & 14 & 554.1292 & \(-\)2.5940 & 0.9986 & 0.0228 \\ \cline{1-1}  & 28 & 465.3938 & \(-\)3.0201 & 0.9972 & 0.0312 \\ \hline \multirow{4}{*}{SI10} & 3 & 75.5010 & \(-\)1.8445 & 0.9998 & 0.0078 \\  & 7 & 93.0119 & \(-\)2.2156 & 0.9996 & 0.0104 \\ \cline{1-1}  & 14 & 39.0152 & \(-\)1.8644 & 0.9984 & 0.0219 \\ \cline{1-1}  & 28 & 82.8129 & \(-\)2.2082 & 0.9984 & 0.0227 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The model performance metrics of the S. and M. model.  
Figure 12: Comparison between the test results and predictions from the optimized model.  
Figure 13: Comparison between the test results and predictions from the optimized model.  
Figure 14: Comparison between the test results and predictions from the optimized model.  
Figure 15: Comparison between the test results and predictions from the optimized model.