## 3 Test Results  
### Model of Compressive Strength Response Surface  
According to the principle of least squares, nonlinear fitting of the response surface test results (Table 3) was performed, and the quadratic polynomial regression equation of the model was established as follows:  
\[Y=\beta_{0}+\sum_{i=1}^{n}\beta_{i}X_{i}+\sum_{i=1}^{n}\beta_{ii}X_{i}^{2}+\sum _{i=1}^{n}\sum_{j=1}^{n}\beta_{ij}X_{i}X_{j} \tag{1}\]  
where \(X\) is the influencing factor of the independent variable; \(Y\) is the response prediction; \(\beta_{0}\) is the constant term; \(\beta_{i}\), \(\beta_{ii}\), and \(\beta_{ij}\) are primary, quadratic, and reciprocal regression coefficients, respectively; \(n\) is the number of factors; and this model has \(n=3\). The relationship between the response predictor and factors influencing the independent variables is as follows:  
\[ \begin{split} Y_{\text{{\it times}}}=-188.53417+27.39592\text{ A}+802.62733\text{ B}-4.63934\text{ C}-13.62045\text{ A}\times\text{B}-\\ 0.057558\text{A}\times\text{C}+0.068599\text{ B}\times\text{C}-2.22153 \text{ A}^{2}-393.91650\text{ B}^{2}+0.038635\text{ C}^{2}\end{split}  \tag{2}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Testing Instruments** & **Manufacturer** & **Model** & **Condition** \\ \hline Unconfined & & & & \\ compression testing & & & & \\ XRD & Hitachi, Tokyo, Japan & Regulus8100 & Powder \\ SEM & Bruker, Karlsruhe, Germany & Bruker D8 & Block \\ CT & Zeiss Xradia, Turingen, Germany & 410 Versa & Cylinder \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of testing instruments. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{3}{c}{**Coding**} & \multicolumn{3}{c}{**Unconfined Compression Strength/kPa**} \\  & **A** & **B** & **C** & **3 Times** & **7 Times** \\ \hline
1 & 2 & 2 & 2 & 51.6678 & 165.59 \\
2 & \(-2\) & 2 & \(-2\) & 55.8221 & 130.526 \\
3 & \(-2\) & \(-2\) & 2 & 51.5718 & 133.779 \\
4 & 0 & 0 & 0 & 94.6443 & 280.631 \\
5 & 2 & 2 & \(-2\) & 52.7002 & 123.431 \\
6 & \(-2\) & 2 & 2 & 62.544 & 225.698 \\
7 & \(-2\) & \(-2\) & \(-2\) & 48.8828 & 32.4845 \\
8 & 0 & 0 & 0 & 89.6984 & 220.61 \\
9 & 0 & 0 & 0 & 119.99 & 275.886 \\
10 & 0 & 1 & 0 & 53.3965 & 286.71 \\
11 & 1 & 0 & 0 & 79.9267 & 227.439 \\
12 & 2 & \(-2\) & 2 & 66.4815 & 80.6484 \\
13 & 0 & \(-1\) & 0 & 86.8894 & 212.578 \\
14 & 0 & 0 & 1 & 92.9203 & 260.159 \\
15 & 0 & 0 & 0 & 85.7327 & 252.046 \\
16 & \(-1\) & 0 & 0 & 108.488 & 291.112 \\
17 & 0 & 0 & \(-1\) & 127.513 & 220.246 \\
18 & 2 & \(-2\) & \(-2\) & 74.4568 & 31.7402 \\
19 & 0 & 0 & 0 & 96.445 & 224.499 \\
20 & 0 & 0 & 0 & 105.208 & 224.342 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary table of response surface experiment results. \[ \begin{array}{l}Y_{Times}=-313.95883+35.28913\ \text{A}+475.04732\ \text{B}+7.93139\ \text{C} \text{-}3.33212\ \text{A}\times\text{B}-\\ 0.329372\ \text{A}\times\text{C}\text{-}0.080451\ \text{B}\times\text{C}\text{-}7.54617\ \text{A}^{2}-184.28868\ \text{B}^{2}-0.052398\ \text{C}^{2}\end{array}  \tag{3}\]  
where \(Y_{Times}\) and \(Y_{Times}\) are the predicted values of the unconfined compressive strength response of the uranium tailing grouted samples with three and seven grouting rounds, respectively, and A, B, and C are the actual values of the bacteria\(-\)centation ratio, cementing solution concentration, and grouting amount, respectively. The absolute value of the regression coefficient indicates the degree to which factors influencing the independent variables affect the predicted response value. Positive or negative coefficients indicate that the response value increases or decreases due to a change in the influencing factors of the independent variables. The significance of the factors influencing the independent variables on the predicted value of the response in the regression model was generally rated by the P-value.