## Box 4
### Analysis of the Influence of Combined Variable Factors on the Compressive Strength of UHPC  
By integrating the AOA-SVR model with the grid scanning method, this study visualizes the effect of different variable factors on the compressive strength of UHPC in a three-dimensional space. This advanced analysis technique allows for a precise illustration of the combined effects of two variable factors. During the analysis, other variables are fixed at their optimal levels while we observe the changes in these two variables. The results are displayed in intuitive three-dimensional graphs, each detailing how specific variations in the variable factors affect the compressive strength of the concrete. This approach not only highlights the impact of individual variables but also provides a comprehensive analysis of how the interaction between variables jointly determines the final \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mineral Admixtures (\%)**} & \multicolumn{3}{c}{**Experimental Results (MPa)**} \\ \cline{2-4}  & **7d** & **14d** & **28d** \\ \hline
0 & 299.17 & 322.04 & 349.36 \\
10 & 302.16 & 327.66 & 351.21 \\
20 & 307.28 & 335.46 & 355.03 \\
30 & 313.14 & 338.74 & 358.14 \\
40 & 316.21 & 341.05 & 362.31 \\
50 & 320.18 & 344.15 & 357.17 \\
60 & 318.19 & 340.05 & 354.31 \\
70 & 315.24 & 336.91 & 345.48 \\
80 & 311.05 & 332.15 & 341.59 \\
90 & 308.82 & 324.51 & 338.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Effect of mineral admixtures content on the compressive strength of UHPC. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Water-Reducing Agent (\%)**} & \multicolumn{3}{c}{**Experimental Results (MPa)**} \\ \cline{2-4}  & **7d** & **14d** & **28d** \\ \hline
1.7 & 315.21 & 340.25 & 377.58 \\
1.8 & 321.46 & 342.65 & 381.14 \\
1.9 & 326.47 & 348.25 & 385.14 \\
2 & 324.14 & 343.65 & 378.85 \\
2.1 & 317.04 & 337.01 & 371.13 \\
2.2 & 311.78 & 332.69 & 367.18 \\
2.3 & 307.14 & 329.05 & 362.19 \\
2.4 & 300.12 & 326.02 & 357.32 \\
2.5 & 297.31 & 323.05 & 352.78 \\
2.6 & 292.47 & 317.15 & 349.68 \\
2.7 & 286.56 & 314.15 & 345.82 \\
2.8 & 283.16 & 310.14 & 340.65 \\
2.9 & 279.81 & 306.25 & 336.15 \\
3 & 273.67 & 302.12 & 331.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._strength. This analysis method offers a scientific foundation for the ratio design of UHPC, aiding in the optimization of materials used to achieve the desired structural performance. As depicted in Figure 3, this subsection presents five examples that illustrate the influence of various factors on the compressive strength, serving as an important reference for the field of concrete technology. Figure 3a illustrates the effects of the water/binder ratio and steel fiber composition on the compressive strength of UHPC. Steel fibers provide additional support and crack bridging, which can significantly increase compressive strength; however, an excessive amount can reduce the uniformity of the concrete. Similarly, while increasing the water/binder ratio can initially improve the compressive strength, an excessively high ratio can introduce too much water, thereby reducing the strength. Therefore, in preparing UHPC, it is crucial to carefully adjust the steel fiber distribution and water/binder ratio to maximize the material's advantages and prevent performance degradation. Figure 3: Three-dimensional view of the influence of combined factors on the compressive strength of UHPC. Figure 3b demonstrates that the appropriate use of mineral admixtures and superplasticizers significantly impacts the compressive strength of UHPC. Mineral admixtures can enhance strength, particularly when used up to 40%. Superplasticizers improve workability and compactness, thus increasing compressive strength. Nevertheless, excessive use of superplasticizers may decrease strength by interfering with the normal hydration process of the cement. Therefore, moderate use of these admixtures is essential to achieve optimal compressive strength, as excessive amounts can lead to performance deterioration.