# Research on Lateral Deformation Control Criteria of Metro Shield Tunnels with Excessive Ellipticity
## 2 Excessive Transverse Deformation Cases in Ghuangzhou Metro
### Analysis of Monitoring Data
\[\sigma_{sq}=\frac{M_{q}}{0.87h_{0}A_{s}}. \tag{5}\]  
Based on the tunnel construction drawings, the design parameters are as follows: the tunnel segment width \(b\) is 1500 mm; the tunnel segment thickness \(h\) is 300 mm; the protective layer thickness \(c_{s}\) is 35 mm; the reinforcement area \(A_{s}\) is 2383 mm\({}^{2}\); the prestressed reinforcement area \(A_{p}\) is 0; the modulus of elasticity of reinforcement \(E_{S}\) is 200,000 N/mm\({}^{2}\); the effective height of the cross-section \(h_{0}\) is 257 mm; the standardized value of concrete strength \(f_{tk}\) is 2.64 N/mm\({}^{2}\); the characteristic coefficient of force for eccentrically compressed members \(a_{cr}\) is 1.9; the effective tensile concrete cross-section area \(A_{te}\) is 225,000 mm; the nominal \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Upline:** & & & \\ \hline
**Mileage (m)** & **Ring Number** & **Tunnel Defect Statistics** & \
\begin{tabular}{c} **Maximum Crack** \\ **Width (mm)** \\ \end{tabular} &
\begin{tabular}{c} **Current Ellipticity of** \\ **the Tunnel (\%o)** \\ \end{tabular} \\ \hline
15,197 & 5 & No cracks seen & & 4.8 \\
15,195.5 & 6 & 3 Short cracks without & 0.205 & 23.1 \\
15,194 & 7 & 8 Cracks through the top & 2.642 & 30.9 \\
15,192.5 & 8 & No cracks seen & 24.8 \\
15,191 & 9 & 6 Cracks through the top & 0.615 & 11.3 \\
15,189.5 & 10 & No cracks seen & 12.4 \\ \hline
**Downline:** & & & \\ \hline
**Mileage (m)** & **Ring Number** & **Tunnel Defect Statistics** & \
\begin{tabular}{c} **Maximum Crack** \\ **Width (mm)** \\ \end{tabular} &
\begin{tabular}{c} **Current Ellipticity of** \\ **the Tunnel (\%o)** \\ \end{tabular} \\ \hline
15,191 & 9 & No cracks seen & 3.5 \\
15,189.5 & 10 & 6 Cracks through the top & 0.212 & 9.1 \\
15,188 & 11 & No cracks seen & 11.7 \\
15,186.5 & 12 & 3 Top penetration cracks & 0.220 & 13.7 \\
15,185 & 13 & No cracks seen & 6.3 \\
15,183.5 & 14 & 6 Cracks through the top & 0.304 & 16.1 \\
15,182 & 15 & No cracks seen & 15.9 \\
15,180.5 & 16 & No cracks seen & 19.8 \\
15,179 & 17 & No cracks seen & 22.2 \\
15,177.5 & 18 & 6 Cracks through the top & 1.222 & 25.7 \\
15,176 & 19 & No cracks seen & 26.3 \\
15,174.5 & 20 & 7 Top penetration cracks & 0.283 & 27.8 \\
15,173 & 21 & No cracks seen & 26.9 \\
15,171.5 & 22 & 3 Top penetration cracks & 0.231 & 25.4 \\
15,170 & 23 & No cracks seen & 22.4 \\
15,168.5 & 24 & 5 Top penetration cracks & 0.174 & 24.1 \\
15,167 & 25 & No cracks seen & 25.4 \\
15,165.5 & 26 & No cracks seen & 20.2 \\
15,164 & 27 & No cracks seen & 20.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comprehensive information on tunnel cracking in an interval. Figure 4: Expanded view of the defective case. Given the formula above, if the crack width of the tunnel segment \(\omega_{\text{max1}}\) exceeds 0.30 mm, the reinforcement stress surpasses the design value for reinforcement strength. In addition, the tensile reinforcement yields when the crack width \(\omega_{\text{max2}}\) exceeds 0.37 mm. Based on these calculations, there are two tunnel rings in the upstream line with crack widths exceeding 0.37 mm, causing the reinforcement in these areas to yield under tension. Conversely, in the downstream line, one ring has a crack width exceeding 0.37 mm, and another possesses a crack width larger than 0.30 mm but not exceeding 0.37 mm.