## 3 Results and Discussions
### Result of RSM/CCD Analysis
#### 3.3.1 ANOVA Result  
The ANOVA of the cubic models developed from the RSM/CCD model is summarized in Table 6. The established model _F_-values of 5.04 and 12.75 were obtained for the flexural and compressive strength model, respectively, revealing the significance of the model with a _p_-value of 0.0468 for the flexural strength and 0.0064 for the compressive strength. The significance of the models and related terms was checked using a 95% confidence level (i.e., _p_-value \(<\) 0.05). As shown in Table 7, the model terms associated with the flexural strength model were insignificant, with a _p_-value higher than 0.05. Similarly, some model terms in modeling the compressive strength revealed insignificance. But the direct interaction of the PU binder and NS (PU binder \(\times\)_NS_) and square of the PU binder were significant in the model, with _p_-values of 0.0106 and 0.0017, respectively, demonstrating a significant _p_-value less than 0.05. The model's equations for the observed values of all responses of PU-cement mortar modified with NS are expressed in Equations (6) and (7). In the model equations preceding the terms, the synergistic impact of independent parameters on the responses is indicated by negative and positive signs. \[ \begin{split}& f_{t}=+14.04-0.445 PU+0.585 NS-0.825 PU*NS-0.865 PU^{2}-0.4 64 NS^{2}+0.355 PU^{2}*NS\\ &-0.51 PU*NS^{2}\end{split}  \tag{6}\]  
\[ \begin{split}& f_{c}=+50.75-7.4 PU+1.15 NS-2.78 PU*NS-9.69 PU^{2}-0.983 NS^{2}+4.2 PU^{2}*NS+4.61 PU*NS^{2}\end{split}  \tag{7}\]  
where \(f_{t}\), and \(f_{c}\), are the flexural strength (MPa), and compressive strength (MPa), respectively. _PU_ is the polyurethane binder (%), and _NS_ is the Nano silica (%). The statistical indicators utilized to evaluate the performance of the developed models are summarized in Table 7, which is sufficient to assess the model's effectiveness in evaluating the responses and reflecting the goodness-of-fit criteria. The proposed model achieved the model's precision level with statistical indicators. The outcome revealed that the CCD/RSM model is capable of handling models with a large number of free features, and the mechanical strength was estimated with high accuracy (refer to Table 7); the corresponding scatter plots are shown in Figure 9. The responses (flexural and compressive \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Response** & **Variable** & \
\begin{tabular}{c} **Sum of** \\ **Squares** \\ \end{tabular} & **DF** &
\begin{tabular}{c} **Mean** \\ **Square** \\ \end{tabular} & **F-Value** & \(p\)**-Value** & **Significant** \\ \hline Flexural strength & **Model** & 15.09 & 7 & 2.16 & 5.04 & 0.0468 & significant \\  & PU binder & 0.3961 & 1 & 0.3961 & 0.9270 & 0.3799 & \\  & NS & 0.6845 & 1 & 0.6845 & 1.60 & 0.2614 & \\  & PU binder\({}^{\times}\) NS & 2.72 & 1 & 2.72 & 6.37 & 0.0529 & \\  & PU binder\({}^{2}\) & 2.06 & 1 & 2.06 & 4.83 & 0.0793 & \\  & NS\({}^{2}\) & 0.5963 & 1 & 0.5963 & 1.40 & 0.2906 & \\ \hline Compressive strength & **Model** & 618.80 & 7 & 88.40 & 12.75 & 0.0064 & significant \\  & PU binder & 109.52 & 1 & 109.52 & 15.80 & 0.0106 & \\  & NS & 2.64 & 1 & 2.64 & 0.3815 & 0.5639 & \\  & PU binder\({}^{\times}\) NS & 31.02 & 1 & 31.02 & 4.47 & 0.0880 & \\  & PU binder\({}^{2}\) & 259.48 & 1 & 259.48 & 37.42 & 0.0017 & \\  & NS\({}^{2}\) & 2.67 & 1 & 2.67 & 0.3847 & 0.5623 & \\  & PU\({}^{2}\)\(\times\) NS & 23.52 & 1 & 23.52 & 3.39 & 0.1249 & \\  & PU \(\times\) NS\({}^{2}\) & 28.40 & 1 & 28.40 & 4.10 & 0.0989 & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Analysis of variance of the models. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Response** & **R\({}^{2}\)** & **Adj. R\({}^{2}\)** & **Pred. R\({}^{2}\)** & **Mean** & **Std. Dev.** & **COV. (\%)** & **AP** \\ \hline Flexural strength & 0.8760 & 0.7023 & 0.6413 & 13.43 & 0.6536 & 4.87 & 7.3913 \\ Compressive strength & 0.9469 & 0.8727 & 5.1647 & 45.87 & 2.63 & 5.75 & 8.3932 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Statistical indicators and model verification.