## 4 Results
The Peck-settlement-trough over a single tunnel can be estimated by the following formula [47; 48]:  
\[S(x)=S_{max}\exp\left(-\frac{x^{2}}{2i^{2}}\right) \tag{6}\]  
where \(S(x)\) is the vertical settlement of a point which is at a distance of \(x\) from the vertical plane containing the tunnel centerline; \(S_{max}\) is the maximum settlement value, the settlement of the point directly above the centerline of the tunnel; and \(i\) is the horizontal distance from the tunnel centerline to the inflection point of settlement curve, which is also known as the half-width of the settlement trough. Researchers and engineers in China have recommended specific parameters for estimating the settlement in China based on their experience from urban shield-tunneling projects [49; 50; 51; 52]. The width of the Gaussian curve (\(i\)) can be estimated by the following formula [47]:  
\[i=\frac{H}{\sqrt{2\pi}\tan\left(45^{\circ}-\frac{\varphi}{2}\right)}, \tag{7}\]  
where \(H\) is the depth of the tunnel centerline; \(\varphi\) is the internal friction angle of the ground, which is set as 25 degrees for this project. The \(i\) value for the case study is 10.6 m. The maximum settlement (\(S_{max}\)) at the riverbed can be estimated by the following formula:  
\[S_{max}=\frac{\pi R^{2}\eta}{i\sqrt{2\pi}}, \tag{8}\]  
where \(R\) is the radius of the tunnel; \(\eta\) is the ratio of soil volume loss (usually expressed as a percentage), which can be estimated by the following formula [53]:  
\[\mathrm{X}=\mathrm{EW}\times\sin\theta+\mathrm{NS}\times\cos\theta\mathrm{Y} =\mathrm{EW}\times\cos\theta-\mathrm{NS}\times\sin\theta \tag{5}\]0  
where \(H\) is the depth of the tunnel centerline, and \(D\) is the diameter of the tunnel. For side-by-side twin tunnel construction, ground surface settlement and lining stress have increased influence from superimposition effects, as compared to the construction of a single-tunnel. It has been observed in many tunneling projects that surface settlement troughs caused by twin tunnels can have a variety of shapes, unlike single tunnels [44]. Figure 10 indicates that the settlements (~2 cm) at GPS1 and GPS2 (Figure 9) are considerably larger than the predicted ones, while the settlements at other stations are comparable with predicted ones. The reasons causing large riverbed deformations at GPS2 and GPS1 will be further investigated in future studies. Figure 9a,b,c exhibit the horizontal movement of six rover antennas along the tunnel centerline direction. GPS1 recorded a gradual forward movement up to one centimeter starting approximately ten days before the shield arrived at GPS1 (see Figure 7a,b for details); the riverbed began to move backward (rebound) immediately after the shield passed GPS1 and ultimately returned to its original place within one week. The horizontal forth and back movements along the excavation direction were not observed at other GPS sites. Figure 9d,e,f exhibit the horizontal movements of GPS along the lateral direction. GPS2 and GPS4 on the first tunnel showed a 5-mm lateral-shift when the shield passed each site. GPS6 did not show any considerable lateral movement. On the second tunnel, only GPS5 showed an 8-mm shift toward the first tunnel when the shield passed the site; GPS1 and GPS3 did not show any considerable lateral movements. However, GPS2, GPS4, and GPS6 on the first tunnel experienced 5- to 10-mm horizontal movements toward the second tunnel during the excavation of the second tunnel. Owing to the excavation of the second tunnel, an increase in the external load acting on the first tunnel is expected. The greater the tunnel distance, the lower the impact of the second tunnel on the normal force in the first tunnel. Previous investigations indicated that there is a negligible effect of interaction at the ground surface between twin tunnels if the distance between the tunnel centerlines is larger than two and half times the tunnel diameter (2.5 D), which is also called the critical distance [43; 45; 54].