## 3 Engineering Background and Numerical Simulation Modeling
### Numerical Simulation Model Building  
Ansys/APDL is used to build the finite element parametric model of the whole bridge, in which the main arch ring is modeled by SOLID65 3D beam unit; considering that the optimization model needs to be solved iteratively at a later stage, LINK10 nonlinear rod unit is used for the buckle cable, and the modulus of elasticity of the buckle cable is modified based on [PERSON]'s formula to account for the geometric nonlinear effect; the restraint between the buckle cable and the main arch ring is achieved by MPC184 unit (activated rigid beam characteristic); the arch footing end face is solidified by face restraint and the node joint degrees of freedom between arch ring \(i\) and \(i+1\) segments. The buckle tension is applied by applying real constants (initial strain), and the \"cell life and death\" function is introduced to simulate the construction process of cantilever casting of the arch ring. To simplify the calculation process and improve the calculation efficiency, the constraint equations are established between the concrete unit nodes and the force reinforcement unit nodes by the \"caint\" command. The \"caintf\" command automatically selects several  
Figure 8: Effect drawing of main span layout of Shatuo Bridge.  
Figure 10: Construction layout of the buckled anchor cable of Shatuo Bridge (unit: cm).  
Figure 9: Typical cross-section of the main arch circle of Shatuo Bridge (unit: cm): (**a**) Arch foot section, (**b**) L/4 section, (**c**) L/2 section.  
To study the effect of temporary prestressing on the stress regulation of the arch ring section, it is assumed that the stress control indexes [13] of sections 10#\(\sim\)17# are given in Table 2. The corresponding section prestressing quantities are obtained by the iterative solution of the procedure in Section 2.3 given in Table 3.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Arch Segment**} & \multicolumn{3}{c}{**West Bank Main Arch**} & \multicolumn{2}{c}{**East Bank Main Arch**} \\ \cline{2-5}  & **Top Flange (MPa)** & **Bottom Flange (MPa)** & **Top Flange (MPa)** & **Bottom Flange (MPa)** \\ \hline
10\% & 0.5 & 0.5 & 0.5 & 0.5 \\
11\% & 0.5 & 0.5 & 0.5 & 0.5 \\
12\% & 0.5 & 0.5 & — & 0 \\
13\% & 0.5 & 0.5 & — & 0 \\
14\% & 0 & — & 0 & 0 \\
15\% & 0 & — & 0 & 0 \\
16\% & 0 & — & 0 & — \\
17\% & 0 & — & 0 & — \\ \hline \hline \end{tabular}
\end{table}
Table 2: Section stress control index [13].  
Figure 14: Schematic diagram of the arrangement of prestressing beams in the section of the arch ring: (**a**) Single top slab with prestressing tendons, A-A cross-section, (**b**) Single bottom slab with prestressing tendons, B-B cross-section, (**c**) Top and bottom slabs with prestressing tendons at the same time, C-C cross-section.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Arch Segment**} & \multicolumn{3}{c}{**West Bank Main Arch**} & \multicolumn{2}{c}{**East Bank Main Arch**} \\ \cline{2-5}  & **Top Flange (pcs)** & **Bottom Flange (pcs)** & **Top Flange (pcs)** & **Bottom Flange (pcs)** \\ \hline
10\% & 32 & — & 18 & — \\
11\% & 32 & — & 28 & — \\
12\% & 32 & — & — & 10 \\
13\% & 32 & — & — & 10 \\
14\% & 34 & — & 34 & 16 \\
15\% & 34 & — & 34 & 16 \\
16\% & 22 & — & 20 & 0 \\
17\% & 18 & — & 16 & 0 \\ \hline \hline \