# Effect of Mix Proportion Parameters on Behaviors of Basalt Fiber RPC Based on Box-Behnken Model
## 3 Results and Discussion
### Establishment and Verification of Response Surface Model
It can be seen from Table 8 that the coefficient of variance (COV) of three response models were all less than 10%, indicating that the models were reliable and highly repeatable [32]. \[\text{COV}=100\ ^{*}\ (\text{std. dev.})/(\text{mean}) \tag{6}\] \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Property**} & \multicolumn{2}{c}{**\(R1\): Fluidity**} & \multicolumn{2}{c}{**\(R2\): Flexural Strength**} & \multicolumn{2}{c}{**R3: Compressive Strength**} \\ \hline \multicolumn{1}{c}{**Transformation**} & \multicolumn{2}{c}{**None**} & \multicolumn{2}{c}{**Ln (\(R2\))**} & \multicolumn{2}{c}{**(\(R3\))\({}^{2}\)**} \\ \hline \(R^{2}\) & \multicolumn{2}{c}{**0.85**} & \multicolumn{2}{c}{**0.87**} & \multicolumn{2}{c}{**0.86**} & \multicolumn{2}{c}{**0.86**} \\ \hline  & **Estimated** & \(F\) & \(p\) & **Estimated** & \(F\) & \(p\) & **Estimated** & \(F\) & \(p\) \\  & **Coefficient** & **Value** & **Value** & **Coefficient** & **Value** & **Value** & **Coefficient** & **Value** & **Value** \\ \hline Intercept & 6.75 & – & – & 4.14 & – & – & 774.04 & – & – \\ \(A\) & –48.67 & 13.38 & 0.0013 & –0.166 & 3.03 & 0.0962 & –38373.37 & 0.13 & 0.72 \\ \(B\) & 336.67 & 88.79 & \textless{}0.0001 & –4.43 & 80.98 & \textless{}0.0001 & 173,679 & 77.82 & \textless{}0.0001 \\ \(C\) & NS & NS & NS & \textless{}1.007 & 4.82 & 0.0394 & 161,764 & 0.44 & 0.51 \\ \(D\) & –3.58 & 15.15 & 0.0007 & –0.61 & 23.8 & \textless{}0.0001 & 23425.17 & 1.59 & 0.22 \\ \(AD\) & 127.5 & 6.68 & 0.0166 & NS & NS & NS & 125,313 & 11.13 & 0.0033 \\ \(BC\) & NS & NS & NS & NS & NS & \textless{}520,259 & 4.37 & 0.0495 \\ \(BD\) & 675 & 7.49 & 0.0117 & NS & NS & NS & \textless{}505,066 & 7.23 & 0.0141 \\ \(CD\) & NS & NS & NS & \textless{}6.6 & 9.03 & 0.0067 & –198,720 & 15.95 & 0.0007 \\ \(C^{2}\) & NS & NS & NS & 7.21 & 10.6 & 0.0038 & NS & NS & NS \\ \(D^{2}\) & NS & NS & NS & 2.728 & 4.68 & 0.0423 & NS & NS & NS \\ Model & – & 26.30 & \textless{}0.0001 & – & 19.32 & \textless{}0.0001 & – & 14.83 & \textless{}0.0001 \\ Lack of fit & – & 3.76 & 0.1040 & – & 1.28 & 0.4465 & – & 0.96 & 0.5831 \\ \hline \multicolumn{1}{c}{Where factor \(A\) is the sand/binder ratio, \(B\) is the water/binder ratio, \(C\) is the fiber volume and \(D\) is the silica} \\ \multicolumn{1}{c}{} & & & & & & & & \\ \multicolumn{1}{c}{} & & & & & & & & \\ \multicolumn{1}{c}{} & & & & & & & & \\ \multicolumn{1}{c}{} & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameter estimation and ANOVA of response surface model. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Statistical Parameters**} & \multicolumn{1}{c}{**Fluidity (cm)**} & \multicolumn{1}{c}{**Flexural Strength (MPa)**} & \multicolumn{1}{c}{**Compressive Strength (MPa)**} \\ \hline Std. Dev. & 0.99 & 0.03 & 738.06 \\ Mean & 22.09 & 2.90 & 11031.73 \\ Coefficient of Variation (COV, \%) & 3.98 & 0.92 & 5.56 \\ Adeq Precision & 19.76 & 17.48 & 14.48 \\ E\({}_{\textless{}5\%\text{CI}}\) & 1.19 & 0.64 & 3.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Statistical analysis of the experimental results. The adeq precision is a measure of the range in the predicted response relative to its associated error, in other words the signal to noise ratio. Its desired value is four or more. As shown in Table 8, ratio of all models is greater than four, indicating an adequate signal. The models can be used to navigate the design space. The predicted and measured values of fluidity, flexural strength and compressive strength for 29 experimental groups are shown in Figure 2. The green dots represent five central points. The error lines are drawn according to the estimated error value of the 95% confidence interval listed in Table 8. Points above the identity line (line of equality between predicted and measured values) indicated that the predicted value was larger than the measured value, while the points below the identity line indicated that the predicted value was less than measured value.