## 4 Parametric Study by Computational Analysis
### Coupled Effect of Two or More Parameters in \(h\), \(t\), and \(a\)  
To further investigate the impact of the three parameters \(h\), \(t\), and \(a\) on the design of the BUSP structure for enhancing the stress performance of the concrete overlay in the bridge deck, a parameterized analysis will be conducted in this study. The analysis will involve simultaneous variations of \(t\) and \(h\), \(h\) and \(a\), and \(t\) and \(a\). Firstly, we focus on the simultaneous variation of \(h\) and \(t\). Figure 19 illustrates how the stress and displacement of the concrete overlay change with different \(h\) and \(t\) values. In the figure, stress is represented by the black frame, while displacement is denoted by the red frame. Figure 18: The cross-sectional area of the concrete overlay varies with changes in \(h\), \(t\), and \(a\). As seen in Figure 19, the variation of \(h\) and \(t\) values exhibit similar effects in improving the maximum tensile stress of the concrete overlay (when the value is smaller than 100 mm). This characteristic is evident from the diagonal trends observed in the stress reduction of the concrete overlay. However, when it comes to their influence on displacement, \(h\) and \(t\) exhibit different patterns. While both \(h\) and \(t\) contribute to a decrease in displacement, the impact of \(h\) is significantly greater than that of \(t\). This is visually apparent from Figure 19, where the direction of displacement reduction primarily aligns parallel to the \(h\) axis. These findings indicate that adjusting the values of \(h\) and \(t\) can effectively enhance the stress performance of the concrete overlay in the bridge deck. However, it is worth noting that there may be limitations or optimal ranges for these parameters to ensure structural integrity and crack resistance in the concrete overlay. Similar to the simultaneous variation of \(h\) and \(t\), Figure 20 illustrates the changes in stress and displacement of the concrete overlay with variations in \(h\) and \(a\). Comparing Figure 20 with Figure 19 reveals that while an increase in \(h\), \(t\), and \(a\) leads to a decrease in the stress of the concrete overlay (when \(h\) is below 100 mm), their individual impacts on concrete stress differ. When comparing the variations with \(h\), the direction in which the stress decreases most rapidly, as depicted in Figure 19, is closer to the \(h\)-axis, whereas in Figure 20, it is closer to the \(a\)-axis. This indicates that variations in \(t\) have a slightly smaller effect on the stress of the concrete overlay compared to variations in \(h\), while variations in \(a\) have a slightly greater effect. When considering simultaneous variations of \(h\) and \(a\), the trend of maximum vertical displacement of the concrete follows a similar pattern as when considering simultaneous variations of \(h\) and \(t\). This implies that among the three parameters adjusting the value of \(h\) is the most effective in reducing the vertical displacement of the concrete overlay. These observations suggest that optimizing the values of \(h\), \(t\), and \(a\) can effectively enhance the stress performance and reduce displacement in the concrete overlay of the bridge deck. However, further analysis and evaluation are necessary to determine the specific optimal ranges for these parameters that strike a balance between stress reduction, displacement control, and other design requirements for the BUSP structure. Figure 19: The stress and displacement of concrete overlay vary with the variation of \(h\) and \(t\). Figure 21 illustrates the relationship between the stress and displacement of the concrete overlay and the variations in parameters \(t\) (thickness) and \(a\) (another parameter). Upon analyzing Figure 21, it becomes apparent that the variation in parameter a primarily affects the maximum tensile stress experienced by the concrete overlay. Conversely, the variation in parameter \(t\) has a more pronounced influence on the maximum vertical displacement of the concrete overlay.