## 6 Conclusions and Discussion  
The main conclusions are as follows:  
(1) Based on similarity theory and utilizing dimensional analysis, this paper derived the similarity criteria for a simply supported beam bridge under concentrated load and designed the proportional model accordingly. The results show that when the geometric scale is 1:\(k\), and the materials of the proportional model and prototype are the same, the concentrated force on the proportional model is \(1/k^{3}\) of the prototype, and the strain in the proportional model is the same as in the prototype. A 1:5 scale model designed using these similarity criteria can ensure that the experimental results intuitively reflect the actual bridge's flexural fatigue behavior.  
(2) Under cyclic loading, the upper part of the PB-DA is in compression, and the lower part is in tension. The variation in the PB-DA strain from top to bottom is linear, generally conforming to the plane section assumption. With the increase in cyclic load numbers, the beam strain exhibits a two-stage development characteristic, accelerating first and then slowing down, with the boundary point at 200,000 cycles. Increasing the D-A content and concrete strength reduces the PB-DA strain. Compared to the C50 PB-DA with 10% D-A content, increasing the D-A content to 30% or enhancing the concrete strength to C80 significantly reduces both maximum compressive and tensile strains. This indicates that a high proportion of the D-A content can ensure the C50 and C80 PB-DA's work performance.  
(3) Under cyclic loading, the flexural stiffness of the PB-DA degrades. When the number of loading cycles does not exceed 200,000, the flexural stiffness shows a nonlinear rapid decay. Once the loading cycles exceed 200,000, the rate of stiffness degradation significantly decreases and shows a linear trend. Increasing the D-A content across different concrete strength grades can reduce the overall degradation of flexural stiffness, indicating that the D-A content is beneficial in C50 and C80 concrete.  
(4) Under continuously increasing static load, the PB-DA displacement increases exponentially, with a constantly decreasing rate, indicating that the PB-DA will not undergo brittle failure. The larger the D-A content, the smaller the displacement of the PB-DA under the same load. After cracks appear in the PB-DA, the distribution of cracks is uniform. When the D-A content is at 10% and 20%, the cracks are more densely distributed, but at 30%, the crack distribution is sparser. This indicates that a higher proportion of the D-A content can slow down the process of PB-DA failure and reduce the extent of damage.  
This paper focuses on the feasibility of applying a large proportion of the D-A content in C50 prestressed concrete bridges, with C80 prestressed concrete bridges as a comparison. Thus, the analysis of the D-A content in prestressed concrete bridges of more strength grades was not conducted. Additionally, this study did not include a control group without D-A in the experimental design, which will be improved in future work.  
Conceptualization, Z.Z.; software, Z.Z. and H.L.; validation, Z.Z.; investigation, H.L.; writing--original draft preparation, Z.Z.; writing--review and editing, Z.Z.; supervision, H.L.; project administration, Z.Z. All authors have read and agreed to the published version of the manuscript. This study received financial support from the Hebei Province Department of Transportation as a critical research project (No. Y-2010024) and the Major Topics of the China Railway (No. K2023G004). Not applicable. Not applicable. Not applicable. Not applicable. Data Availability Statement: The original contributions presented in this study are included in the article; further inquiries can be directed to the corresponding author. The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.