# 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  
The tunnel commenced operations in December 2006. By the first half of 2020, many rings of tunnel lining segment in the tunnel's left and right lines exhibited widespread and numerous cracks. The most pronounced cracking was observed in ring No. 7 of the upline, as depicted in Figure 2.  
After detecting significant issues in the shield tunnels, laser scanning was employed for monitoring tunnel deformation. The ellipticity monitoring method predominantly uses the GRP5000 mobile laser scanning measurement system for continuous scanning of underground shield tunnels. This approach captures holographic images and data within the specified tunnel section, encompassing tunnel section ellipticity in each ring, vehicle limits, and the tubular segment's surface disease, among other metrics. Ellipticity is derived from the tunnel's deformed short and long axes and is typically determined by the difference between a tunnel's maximum and minimum diameters and its designed internal diameter, expressed in thousandths as a ratio. Since limited research currently exists on the lateral deformation limit of relevant tunnels based on ellipticity, engineering experience generally sets this threshold at 25%. The latest monitoring results prior to reinforcement measures are presented in Figure 3.  
Figure 3: Ellipticity monitoring values of tunnels in cases of defective intervals. Figure 2: Crack map of ring 7 on the upstream line. Multiple shield tunnel rings in the upline and downline of this interval exhibited lateral deformations exceeding the empirical 25%\(\infty\) limit. Specifically, the maximum elliptic deformation on the upline reached 30.9% in one ring, while on the downline, it was 27.8%, impacting six rings. In addition, the uplines and downlines did not exhibit identical mileage regarding the over-limit deformation rings. The deficiency locations were approximately 20 m apart horizontally. Adjacent tunnel rings showing over-limit deformation demonstrated apparent structural issues. Ring No. 7 in the upstream line experienced the most pronounced elliptic deformation at 30.9%, with the most extensive crack measuring around 2.64 mm. Several observations can be made based on the disease distribution map from Figure 4 and comprehensive tunnel cracking data from Table 1. There is a relationship between the number of shield tunnel cracks, crack width, and tunnel lateral deformation. Shield tunnels are prone to cracking when the ellipticity is large, and the larger the ellipticity, the larger the number and width of cracks are likely to be. At the same time, even when tunnel deformation is minimal, multiple minor cracks can appear. Some shield ring deformations exceeding the general 25% limit did not exhibit apparent cracks. However, the location of these cracks is consistent, predominantly at the top of the shield tunnel ring, with the crack direction mainly being longitudinal. The tunnel's waist sides are susceptible to leakage and other structural issues. According to the Design Code for Concrete Structures GB50010-2010 (2015 Edition) specifications [18], the width of concrete cracks can be estimated using the following Equations (1)-(5):  
\[\omega_{\max}=\alpha_{cr}\psi\frac{\sigma_{\mathrm{s}}}{E_{S}}\left(1.9c_{s} +0.08\frac{d_{eq}}{\rho_{te}}\right), \tag{1}\]  
\[\psi=1.1-0.65\frac{f_{tk}}{\rho_{te}\sigma_{\mathrm{s}}}, \tag{2}\]  
\[d_{eq}=\frac{\sum n_{i}d_{i}^{2}}{\sum n_{i}\
u_{i}d_{i}}, \tag{3}\]  
and  
\[\rho_{te}=\frac{A_{s}+A_{p}}{A_{te}}, \tag{4}\]  
where \(\omega_{\max}\) is the maximum crack width affected by the long-term effects. The tensile stress in the tension zone can be derived using the following equation for the concrete segmental lining's bending components.