# Simulation of Test Arch Based on Concrete Damage Plasticity Model and Damage Evolution Analysis
## 4 Simulation Model Construction
### Initial Damage Simulation Approach  
Before conducting the analysis, it is essential to assess the arch ring stress variation throughout the construction phase and pinpoint potentially vulnerable cross-sections. Three cast-in-place arch bridges were selected for comparison: Shatuo Bridge (with a span of 240 m), Qingshui River Bridge (with a span of 248 m), and Xixiu Bridge (with a span of 288 m). The stress changes during the construction of the three bridges are shown in Figure 9. The data suggested that as the length of the constructed segments increased, the peak stress on the upper edge progressively relocated towards the crown of the arch. Notably, most bridges manifested significant tensile stress concentrations at this crown. Conversely, while stress variations were evident at the lower edge near the abutment, they predominantly clustered in its vicinity. These findings underscored the arch crown as a pivotal transition point during construction. Before commencing construction at the crown segment, primary damage locations were predominantly at the base plate of abutments. However, after this phase, these points shifted closer to the top plate of the crown.  
Drawing from the original experimental data and stress calculations during the bridge's construction phase, this study identified the springing and hance locations of the load points as focal areas for damage simulation. In line with our predetermined simulation approach, four damage categories were established: top slab at springing (working condition I), bottom slab at springing (working condition II), top slab at hance (working condition III), and bottom slab at hance (working condition IV). Each damage category encompassed three models, reflecting loss rates of 5%, 10%, and 15%, culminating in 12 distinct models.  
Concrete damage simulation predominantly employs methodologies, such as CIT, VCCT, XFEM [27; 28; 29], and the damage mechanics-based CDP model [30]. Given our emphasis on macroscopic effects on the overarching bridge structure, local crack propagation was not a component of this study. Consequently, utilizing the CDP plastic damage model, specific structural elements were pinpointed and a Python code was devised to simulate concrete material damage through random porosity. The detailed mesh of this model is depicted in Figure 10.  
The protective layer of the arch rib has a thickness of 10 mm. Considering the potential full-layer damage, a 16 mm concrete thickness was designated for the simulation. The element size was set at 4 mm and a 12 mm thickness was earmarked for element removal, excluding elements proximate to the contact surface from damage consideration. The damage zone was an independent mesh component seamlessly integrated with the arch rib. To optimize computational efficiency, the mesh was meticulously segmented within the arch rib's damage simulation zone, progressively increasing the mesh size through a transitional area.  
Figure 8: Comparison of damage distribution in the left half-span for Case 13: (**a**) test model [16]; (**b**) simulation model.