# Simulation of Test Arch Based on Concrete Damage Plasticity Model and Damage Evolution Analysis
## 2 Overview of the Experiment  
The simulation model was constructed based on the scaling test done by [PERSON] of Southwest Jiaotong University [16]. The prototype for this model is the Damotan Bridge on the Longna Line in Sichuan. Scaled down to 1/10 of the original, the test arch spans 450 cm, with a net sagittal span ratio of 1/6 and an arch axis coefficient of m = 1.756. The arch rib section measures 8 cm in width and 11 cm in height and is constructed using C40 standard concrete. The section edges of the arch foot, both upper and lower, are reinforced with three \(\Phi\)6 bars, resulting in a reinforcement rate of 1.93%. Conversely, the section edges of the vault are reinforced with two \(\Phi\)6 bars, achieving a 1.29% reinforcement rate.  
Based on the scaled-down calculations, the dead load compensation for the self-weight of the arch rib and the converted dead load from the structure atop the arch are detailed in Table 1. These loads are applied at loading points 1# to 13#. According to the research objectives in the literature [16], the reason for selecting #1 and #2 columns as loading points is to analyze the structural forces at the foot of the arch for the maximum bending moment condition. Consequently, the test live load is specifically applied at points 1# and 2#. Positions 3#\(\sim\)13# have dead loads applied by counterweights, while positions 1# and 2# both use jacks to apply dead loads and live loads. A schematic representation of the loading arrangement is displayed in Figure 1. Arch rib section is displayed in Figure 2.  
According to the literature [16], there were 13 loading conditions in the experiment, and their corresponding values are listed in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **1\# Point** & **2\# Point** & **Cumulative** & & **1\# Point** & **2\# Point** & **Cumulative** \\  & **Loading** & **Loading** & **Live Load** & **Number** & **Loading** & **Loading** & **Live Load** \\  & **Value (kN)** & **Value (kN)** & **Multiplier** & & **Value (kN)** & **Value (kN)** & **Multiplier** \\ \hline
1 & 1.82 & 1.99 & 0.40 & 8 & 0.86 & 1.28 & 1.88 \\
2 & 2.04 & 2.15 & 0.84 & 9 & 1.00 & 0.78 & 2.07 \\
3 & 1.15 & 0.78 & 1.04 & 10 & 0.87 & 0.90 & 2.25 \\
4 & 0.79 & 0.86 & 1.21 & 11 & 1.03 & 1.41 & 2.51 \\
5 & 1.23 & 1.07 & 1.45 & 12 & 1.16 & 0.94 & 2.73 \\
6 & \(-\)0.28 & 0.00 & 1.42 & 13 & 1.01 & 0.84 & 2.92 \\
7 & 1.32 & 0.98 & 1.66 & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Numerical values of live load for each working condition of the test arch.  
Figure 1: Basic arrangement of test arch (unit: cm).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{5}{c}{**Dead Load Values**} & \multicolumn{4}{c}{**Live Load Values**} \\ \hline
**Loading Point** & **Load (kN)** & **Loading Point** & **Load (kN)** & **Loading Point** & **Load (kN)** \\ \hline
1\# & 5.48 & 8\# & 1.07 & 1\# & 4.79 \\
2\# & 3.79 & 9\# & 1.23 & 2\# & 4.79 \\
3\# & 3.49 & 10\# & 1.33 & & & \\
4\# & 1.33 & 11\# & 3.49 & & & \\
5\# & 1.23 & 12\# & 3.79 & & & \\
6\# & 1.07 & 13\# & 5.48 & & & \\
7\# & 3.08 & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Load values of the test arch.  
Figure 2: Section dimensions and reinforcement arrangement [16] (unit: cm): (**a**) section of the foot of the arch; (**b**) L/4 and vault section.