## 3 Comparison between Proposed Full-Ring Model and Experiments
### Comparison of Internal Forces and Deformations
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experimental Case** & **Soil Overburden (m)** & **Coefficient of Lateral Pressure** & **Ground Overload (kPa)** & **Experimental Load (kN)** \\ \hline \multirow{2}{*}{1} & \multirow{2}{*}{8} & 0.7 (soil-water together) & \multirow{2}{*}{20 kPa} & P1 = 300, & \\  & & & & P2 = 170, & \\  & & & & P3 = 212 & \\ \hline \multirow{2}{*}{2} & \multirow{2}{*}{17} & 0.4 (soil-water separately) & \multirow{2}{*}{20 kPa} & P1 = 450, & \\  & & & & P2 = 250, & \\  & & & & P3 = 355 & \\ \hline \multirow{3}{*}{3} & \multirow{3}{*}{17} & \multirow{3}{*}{0.7 (soil-water together)} & \multirow{3}{*}{20 kPa and partial offset load of 30 kPa} & P1 = 481, P2 = 227, P3 = 503, & \\  & & & & P4 = 458, P5 = 344, P6 = 599 & \\ \cline{1-1}  & & 0.7 (soil-water together) & \multirow{3}{*}{20 kPa and partial offset load of 30 kPa} & P7 = 400, P8 = 486, P9 = 406 & \\ \cline{1-1}  & & & & P10 = 239, P11 = 255, P12 = 388 & \\ \cline{1-1}  & & & & P13 = 489, P14 = 40, P15 = 387 & \\ \cline{1-1}  & & & & P16 = 258 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Full-scale ring experimental cases. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Experimental** & \multicolumn{2}{c}{**Convergence**} & \multirow{2}{*}{**Experiment (mm)**} & \multirow{2}{*}{**Model (mm)**} & \multicolumn{2}{c}{**Ratio**} \\
**Case** & **Displacement** & & & **(Model/Experiment)** \\ \hline \multirow{4}{*}{1} & D1 & \(-\)4.74 & \(-\)4.43 & 0.93 \\  & D2 & 4.68 & 4.51 & 0.96 \\  & D3 & \(-\)6.92 & \(-\)7.06 & 1.02 \\ \hline \multirow{4}{*}{2} & D1 & \(-\)6.37 & \(-\)7.00 & 1.10 \\  & D2 & 8.44 & 8.72 & 1.03 \\  & D3 & \(-\)12.61 & \(-\)12.34 & 0.98 \\ \hline \multirow{4}{*}{3} & D1 & \(-\)1.87 & \(-\)2.21 & 1.18 \\  & D2 & 9.24 & 9.01 & 0.98 \\  & D3 & \(-\)19.68 & \(-\)18.41 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of convergence deformations. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & \multicolumn{2}{c}{**Experiment**} & \multicolumn{2}{c}{**Model**} & \multicolumn{2}{c}{**Ratio**} \\
**Experimental** & **Key** & \multicolumn{2}{c}{**Section**} & \multicolumn{2}{c}{**Bending**} & \multicolumn{2}{c}{**Axial**} & \multicolumn{2}{c}{**Bending**} & \multicolumn{2}{c}{**Axial**} \\
**Case** & **Section** & \multicolumn{2}{c}{**Moment**} & \multicolumn{2}{c}{**Force (kN)**} & \multicolumn{2}{c}{**Moment**} & \multicolumn{2}{c}{**Force (kN)**} & \multicolumn{2}{c}{**Moment**} & \multicolumn{2}{c}{**Force (**\(k\)**)**} \\
**1** & **M1** & \(-\)289 & \(-\)631 & \(-\)269 & \(-\)635 & 0.93 & 1.01 \\  & JM2 & 237 & \(-\)628 & 231 & \(-\)602 & 0.97 & 0.96 \\  & JM3 & \(-\)121 & \(-\)71  
From the comparison of the numerical and experimental results in these three cases with different load levels, it can be concluded that the model established in this paper can evaluate the mechanical behavior of a quasi-rectangular lining structure with good accuracy. The developed model is verified for the quasi-rectangular shield tunnel of Figure 2, whose outline consists of four specific arcs, with ten segments and one interior column. However, the authors are confident that the method considering nonlinear behavior of the joints is applicable for other special-section shield tunnels as well.