## 3 Analysis of Test Results  
### Test Results  
Table 6 summarizes the uniform test results, where the sequence combination was obtained from Table 5, and the performance of the slurry is jointly governed by six factors: water-binder ratio (\(x_{1}\)), binder-sand ratio (\(x_{2}\)), fly flash-cement ratio (\(x_{3}\)), soil-binder ratio (\(x_{4}\)), particle size (\(x_{5}\)), and water-reducing admixture content (\(x_{6}\)). To analyze these relationships, a regression analysis was performed on the test data in Table 6 using the [PERSON] second-order polynomial mix specification in SPSS software (SPSS Statistics 27.0.1), as outlined in Equation (1) through (6), where the particle size (\(x_{5}\)) was input as the average within a specific range. This approach enables an understanding of how the individual and interactive effects of these variables influence the performance of slurry.  
\[f_{n}=B_{0}+\sum_{i=1}^{m}B_{i}x_{i}+\sum_{i=1}^{m}B_{ii}x_{i}^{2}+\sum_{i=1}^ {m}B_{ij}x_{i}x_{j} \tag{1}\]  
where \(f_{n}\) represents the response observed, encompassing properties such as the density, setting time, bleeding rate, consistency, fluidity, and strength. The coefficients \(B_{i}\) and \(B_{\bar{u}}\) correspond to the regression coefficients. \(B0\) is the constant of the regression equation, while xi and xj denote the experimental factors.  
Figure 5: Determination of basic properties of grout. (**a**) Density; (**b**) bleeding rate; (**c**) consistency; (**d**) fluidity; (**e**) setting time; (**f**) strength.  
Density:  
\[\begin{split} f_{1}=2.268-0.762x_{1}^{2}+0.026x_{3}^{2}-0.109x_{4}^{2} -0.4x_{3}+0.342x_{1}x_{3}+\\ 0.473x_{1}x_{4}-0.498x_{2}x_{5}-0.074x_{3}x_{4}+0.203x_{3}x_{5}\end{split} \tag{2}\]  
Bleeding rate:  
\[\begin{split} f_{2}=-6.768+6.272x_{4}^{2}+18.366x_{1}-14.341x_{5}- 2.434x_{1}x_{3}-20.317x_{1}x_{4}+\\ 50.925x_{1}x_{5}-12.070x_{2}x_{5}+3.420x_{3}x_{4}-18.488x_{4}x_{5} \end{split} \tag{3}\]  
Fluidity:  
\[\begin{split} f_{3}=26.617-1.771x_{3}^{2}-150.019x_{6}-25.359x_{2} x_{4}-5.55x_{3}x_{4}+8.929x_{1}x_{3}\\ +85.372x_{3}x_{6}+6.514x_{1}x_{4}\end{split} \tag{4}\]  
Consistency:  
\[\begin{split} f_{4}=16.920-0.926x_{3}-25.550x_{4}+23.256x_{1}x_{ 4}-1.335x_{3}x_{4}-99.789x_{2}x_{6}+\\ 39.864x_{3}x_{6}\end{split} \tag{5}\]  
Setting time:  
\[\begin{split} f_{5}=-2199.459+2714.710x_{2}^{2}+1040.001x_{4}^{2} +7119.275x_{1}-\\ 5283.061x_{1}x_{2}-3521.543x_{1}x_{4}\end{split} \tag{6}\]  
Slurry strength:  
\[\begin{split} f_{6}=-2.429-3.916x_{1}^{2}+0.312x_{3}^{2}+14.007x_ {2}+4.212x_{4}+4.067x_{1}x_{2}-4.359x_{2}x_{3}\\ -8.091x_{2}x_{4}+0.688x_{3}x_{4}+0.703x_{4}x_{5}\end{split} \tag{7}\]  
The regression analysis outcomes are shown in Table 7. Key metrics include MS for mean square, SS for sum of squares deviation from the mean, and DF for degree of freedom. An R2 nearing 1 signifies a superior fit, suggesting that the independent variable is better able to elucidate variations in the test results through the regression model [49]. Furthermore, the goodness of fit of the regression equation is assessed by the concordance between R2 and adjusted R2 values. A narrow gap between adjusted R2 and predicted R2 signifies the predictive significance of the model [50]. The F-test evaluates the statistical significance of the regression equation, with higher F-values and \(p\)-values below 0.05 indicating greater equation significance.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**No.** & **w/b** & **b/s** & **f/c** & **so/b** & **Particle Size** & **SPs** & **Sequence** & **Density** & **Setting** & **Bleeding** & **Fluidity** & **Consistency** & **Strength** \\  & & & & & & & & & & & & & & \\
1 & 0.6 & 0.55 & 3 & 0.6 & 0.5–0.3 & 0.015 & 125,312 & 1.78 & 3.9 & 0.60\% & 12.5 & 4.78 & 2.07 \\
2 & 0.7 & 0.6 & 1 & 0.4 & 0.085–0.0 & 0.045 & 231,254 & 1.85 & 10.82 &