## 3 Selection of Input Variables for Influencing Factors of Mechanical Properties of UHPC
### Box 1  
Table 1 shows the relationship between the water/cement ratio and the strength of UHPC. It can be observed that the unique properties of UHPC are partly attributed to its extremely low water/cement ratio, which significantly enhances the compactness and strength of concrete. Between the water/cement ratios of 0.14 and 0.2, as the water/cement ratio increases, the strength of UHPC exhibits a certain linear growth, which may be due to the moderate increase in the water/cement ratio reducing internal defects and initially improving the strength of UHPC. However, when the water/cement ratio exceeds 0.2, the strength no longer increases but instead shows a downward trend. Specifically, the strength reaches a peak at a water/cement ratio of 0.21, but the strength is significantly reduced when the water/cement ratio is further increased to 0.22 and 0.23. This nonlinear relationship indicates that although moderately increasing the water/cement ratio can improve the performance of UHPC, excessively high water/cement ratio will reduce the efficiency of the hydration reaction and cause a decrease in concrete strength. Therefore, it is crucial to determine an optimal water/cement ratio range. Our experimental data and analysis results show that the strength of UHPC is the highest when the water/cement ratio is between 0.19 and 0.2, which provides important guidance for the design and application of UHPC, indicating that optimal performance can be achieved by appropriately adjusting the water/cement ratio. Remarks Content:  
Our experimental data was collected and compiled from a number of published studies on ScienceDirect and Google Scholar databases. These studies all conducted detailed tests on the compressive strength of ultra-high-performance concrete (UHPC) and reported specific results under different water/cement ratios. We extracted and compiled the relevant data from these published studies with the aim of conducting a more systematic analysis of the relationship between UHPC compressive strength and water/cement ratio. All test samples were 100 mm \(\times\) 100 mm \(\times\) 100 mm cubic specimens, a standardized size widely used in experimental testing of concrete compressive strength. By using standard-sized specimens, we ensured the comparability and reliability of the test results. For each water/cement ratio condition, at least three specimens were prepared, and their compressive strength was tested at 7 days, 14 days, and 28 days. We used the average of the three test results as the final data to ensure the accuracy and reproducibility of the data. All compressive strength tests were conducted in accordance with the international standard ASTM C39/C39M-18, \"Standard Test Methods for Compressive Strength of Hardened Concrete\". The specimens were cured under standard curing conditions (temperature 20 \(\pm\) 2 \({}^{\circ}\)C, relative humidity of not less than 95%), and their compressive strength was tested at 7 days, 14 days, and 28 days, respectively. A hydraulic pressure testing machine was used in the test, and the loading speed was strictly controlled at 0.25 MPa/s to ensure the consistency and scientificity of the test conditions. Through this systematic analysis of the data, we can have a comprehensive understanding of the trend of UHPC compressive strength under different water/cement ratio conditions and verify the accuracy and applicability of the model we proposed. All experimental data in Tables 2-4 are from the same sources as the test standards in Table 1.