# Calculation Method of New Assembled Corrugated Steel Initial Support Structure of Highway Tunnel
## 2 Full-Scale Test of Corrugated Steel
### Test Results and Analysis
#### 2.2.2 Comparative Analysis between Test and Simulation  
As shown in Figure 4, a finite element (FE) model was constructed in ABAQUS to replicate the dimensions of the full-scale test setup. (1) Meshing: Grid sizes were selected to minimize computational costs while ensuring calculation accuracy. Following multiple simulations, a grid size of 3 mm was chosen for the CSP, ensuring a minimum of two grid divisions in the thickness direction. Solid elements (C3D8R) were utilized to model the CSP and supports. (2) Interaction: The bolts were primarily responsible for securing the support and corrugated steel as a unified assembly. Due to the intricate contact interactions among bolts, CSP, and support, tie contact was utilized to link the peaks and troughs of the CSP to the support, serving as an alternative to the bolts. Hard contact was established between the side of the corrugated steel and the support. \"Tie contact\" means that the selected sets of points will not experience relative displacement. \"Hard contact\" means that the selected surfaces cannot penetrate each other in the normal direction, with tangential behavior following [PERSON]'s friction law, where the friction coefficient between the steel was set to 0.1. (3) Boundary conditions: The left side of the left support restricts horizontal displacement, and the rollers under supports restrict vertical displacement. The roller on the right side of the right support was subjected to axial force. (4) Material properties: the constitutive relationships governing bolts, CSP, flanges, and supports followed an elastic-plastic hardening model, details of which are provided in Table 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Support**} & \multicolumn{2}{c}{**Corrugated Steel**} & \multicolumn{2}{c}{**Bolt**} \\
**Stress/MPa** & **Strain/\(\epsilon\)** & **Stress/MPa** & **Strain/\(\epsilon\)** & **Stress/MPa** & **Strain/\(\epsilon\)** \\ \hline
0 & 0 & 0 & 0 & 0 & 0 \\
400 & 0.002 & 310 & 0.00155 & 640 & 0.0032 \\
540 & 0.1532 & 440 & 0.132 & 800 & 0.1532 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Elastic–plastic hardening constitutive model. Figure 4: Schematic illustration of three-dimensional refined FE model of corrugated steel plate. Based on the mechanical test data of CSP, Figure 5 compares numerical simulation and experimental results. The vertical load-deflection curve from the full-scale mechanical test of CSP exhibits two distinct stages differentiated by changes in slope: clearance elimination and elastic stages. (1) During the gap elimination stage, initial gaps between the CSP and the loading system resulted in inelastic deformation. The initial loading primarily served to eliminate these gaps, characterized by a significant gap, low stiffness, and substantial deformation under equivalent forces, causing a steep slope in the curve. (2) In the elastic stage, as the gaps observed in the first stage were compressed, the CSP specimen consolidated into a unified structure, thereby increasing structural stiffness. Consequently, the slope of the curve becomes gentler, indicating effective engagement of the corrugated structure. As a prefabricated structure, the corrugated steel samples initially exhibited gaps. During the initial loading phase of the test, these gaps were eliminated. Once the gaps were closed, the sample transitioned into the elastic stage. In contrast, the FE model was perfectly assembled with no initial gaps, allowing it to enter the elastic phase directly. The slope of the vertical load-deflection curve during the experimental elastic phase is consistent with that of the numerical calculation model. The vertical load-deflection curve from the numerical simulation closely parallels what was observed during the elastic stage of the full-scale test. A comparison of average midspan deflection values between the numerical simulation and the mechanical test reveals minimal disparity.