## Box 4
### Analysis of the Influence of Combined Variable Factors on the Compressive Strength of UHPC
Figure 3c shows that in the preparation of UHPC, the water/binder ratio and water-reducer dosage are critical factors that directly influence the compressive strength. Moderately increasing the water/binder ratio (from 0.15 to 0.20) can significantly boost strength by promoting full cement hydration and enhancing the concrete structure. However, beyond this critical value, the rate of strength increase slows down because a higher water/binder ratio increases concrete porosity. As the dosage of water-reducing agent increases to 1.5%, the strength of UHPC improves. Nevertheless, when the dosage exceeds 2.5%, the strength peaks, and further increases in the water-reducer dosage may lead to a reduction in strength. Figure 3d demonstrates that the precise dosage of steel fiber and mineral admixtures is crucial for optimizing the compressive strength of UHPC. As the proportion of steel fiber increases to 3.0%, the strength significantly improves, indicating an optimal proportion point. Additionally, the moderate addition of mineral admixtures can increase the strength, but their positive effect diminishes after reaching a maximum value, potentially leading to a performance decline. When the steel fiber content reaches approximately 6.0%, the compressive strength initially decreases and then increases, highlighting the complex interactions between materials. Therefore, in designing UHPC, it is essential to precisely control the amounts of steel fiber and mineral admixtures to maximize performance while enhancing economic efficiency and environmental sustainability. Figure 3e illustrates the effect of steel fiber length on the compressive strength optimization of UHPC. Considering the significant influence of the length of steel fibers on the compressive strength of UHPC [15; 16], a comprehensive investigation was conducted to explore the effect of steel fiber length on the compressive strength of UHPC. The results indicate that as the length of steel fibers increases, the compressive strength also increases. This is because longer fibers can more effectively bridge micro-cracks, enhancing the toughness and crack resistance of the concrete. However, when the steel fiber length reaches approximately 8 mm, the growth in compressive strength begins to diminish. This reduction in growth trend may be due to difficulties in the distribution and orientation of excessively long fibers within the mix. Additionally, longer steel fibers increase material costs, necessitating a balance between economic benefits and performance improvement to determine the optimal fiber length and dosage. From the above three-dimensional diagrams, it is evident that the constructed machine learning model effectively analyzes how variations in water/binder ratio and steel fiber, mineral admixtures and superplasticizers, water/binder ratio and superplasticizers, and steel fiber and mineral admixtures influence the compressive strength of UHPC. This predictive analysis unveils the complex interactions among each component, providing a valuable reference for engineering applications.