## 3 Numerical Validation and Results
### Prestress Loss  
The investigation focuses on the impact of prestress loss in various tendons on bridge performance, with prestress loss rates determined at 33.3%, 66.7% and 100% of the average values listed in Table 4. The adopted case is presented in detail in Table 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Analysis Case**} & \multicolumn{2}{c}{**Horizontal Prestress**} & **Vertical Prestress** & **Longitudinal Prestress** \\  & & **Loss Rate (\%)** & **Loss Rate (\%)** & **Loss Rate (\%)** \\ \hline \multirow{3}{*}{Horizontal and vertical prestress loss combinations} & Case I & \(15.1\) & 22.9 & - \\  & Case II & 30.3 & 45.7 & - \\  & Case III & 45.4 & 68.6 & - \\ \hline \multirow{3}{*}{Longitudinal prestress loss conditions} & Case IV & - & - & 9.7 \\  & Case V & - & - & 19.3 \\ \cline{1-1}  & Case VI & - & - & 29.0 \\ \hline \multicolumn{2}{c}{No loss condition} & Case VII & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of the prestress loss case. Figure 14: Deflection for different creep ages. Figure 16 illustrates the deflection relationship under various prestress loss conditions. It is evident that the combined horizontal and vertical prestress loss had a negligible impact on the overall deformation performance of the bridge, except for its effect on local force and the deformation of the box girder, which will be discussed in detail later. However, longitudinal prestress loss exerted a significant influence on overall stiffness. Compared with the no-prestress-loss condition, the maximum deflection of the main-span bridge increased by 87.2%, 172.8%, and 260.0% for Case IV, Case V, and Case VI, respectively. After a comprehensive comparison of the aforementioned four types of damage behaviors, it can be concluded that the primary cause for long-lasting deflection in continuous rigid frame bridges is attributable to the time-dependent loss of longitudinal prestress. In detail, sensitivities to the impact on the overall performance of the structure ranged from significant to slight: longitudinal prestress loss, box girder crack, concrete creep, continuous joint damage, and horizontal and vertical prestress loss to discrete joint damage, respectively. Figure 16: Deflection for different prestress loss conditions. Figure 15: Deflection for different joint damage conditions. Firstly, the influence of box web crack on local stress was investigated. The stress distribution results of perfect and cracked box girder elements at the same location are presented in Figure 17a. It is evident that the occurrence of a crack within the box girder leads to local stress redistribution, with the region of tension failure (stress exceeding 3 MPa) initially occurring adjacent to and below the position of the crack. Additionally, with the appearance of cracks, the uneven degree of stress distribution increased and stress concentration appeared near the crack location. The impact range of concrete cracking in a single section on the structural stress contour is summarized in Figure 17b. It can be observed that the effect of box girder crack at the quarter point on stress distribution was limited, and there was a more pronounced redistribution of stress on the left side of the crack than on the right side, indicating that web cracks have a greater effect on shear-moment coupling zone mechanical properties. Figure 18 depicts the axial stress and vertical displacement distribution under different loading ages of concrete. It can be concluded that the amplitude and distribution law were similar under different concrete creep ages, except for the displacement value. It is suggested that the time-dependent behavior of concrete has little impact on the overall distribution of structural stiffness, with only a slight reduction in stiffness observed.