## 4 Results  
Ground settlement resulting from constructions of twin tunnels has been subjected to extensive investigations [43; 44; 45; 46]. It is beyond the scope of this paper to speculate how excavation of the tunnel induced riverbed deformation, and how excavation of the second tunnel interacted with the first tunnel. However, a quick look at the displacement time series does give some impressive results that may help to understand the complexity of the riverbed deformation during shallow tunneling. In order to track the riverbed displacements in the directions along and across the tunnel centerline, the previous horizontal EW-NS coordinate system was rotated by 63.7 degrees clockwise (\(\theta=-63.7^{\circ}\)) to form an X-Y coordinate system as shown in Figure 8.  
\[\mathrm{X}=\mathrm{EW}\times\sin\theta+\mathrm{NS}\times\cos\theta\mathrm{Y} =\mathrm{EW}\times\cos\theta-\mathrm{NS}\times\sin\theta \tag{5}\]  
After the rotation, the X-axis is parallel to the excavation direction, and the Y-axis is perpendicular to the excavation direction. The displacement time series with respect to the rotated coordinate system of these six rover antennas are illustrated in Figure 9. The displacements are derived from daily DD solutions referred to the base station. The dates that the shield passed the GPS sites are plotted on each subfigure. Those dates are also listed in Table 1.  
Figure 7: Plots demonstrating the implementation of the change point detection (CPD) algorithm to aid in detecting abrupt and gradual displacements superimposed into the hourly positional time series of GPS1. The shield machine passed GPS2, GPS4, and GPS6 sites on 28 April, 4 May, and 15 May 2018, respectively, during the excavation of the first tunnel. Only GPS2 recorded an abrupt settlement  
Figure 8: (**a**) The coordinate rotation from the EW–NS coordinates to the X–Y coordinates; (**b**) The X-axis aligns with the centerline of the tunnel, and the positive direction indicates the shield driven direction; the Y-axis aligns with the lateral direction that is perpendicular to the tunnel centerline. Figure 9: GPS-derived daily displacement time series at six rover GPS sites with respect to the base station. (**a**), (**d**), and (**g**) illustrate the displacement time series of GPS1 and GPS2 in the directions along tunnel-axis, cross tunnel-axis, and vertical, respectively; (**b**), (**e**), and (**h**) illustrate the displacement time series of GPS3 and GPS4 in the directions along tunnel-axis, cross tunnel-axis, and vertical, respectively; (**c**), (**f**), and (**i**) illustrate the displacement time series of GPS5 and GPS6 in the directions along tunnel-axis, cross tunnel-axis, and vertical, respectively. of approximately 2 cm within one week after the shield passing this site. GPS4 and GPS6 did not record any considerable immediate settlement after the shield passing. The shield machine passed GPS1, GPS3, and GPS5 on 26 May, 4 June, and 13 June 2018, respectively, during the excavation of the second tunnel. GPS1 recorded an abrupt settlement of approximately 2.2 cm within four days after the shield passing. GPS3 and GPS5 recorded minor abrupt settlement of approximately 0.5 cm within one week after the shield passing. GPS2, GPS4, and GPS6 on the first tunnel did not record any considerable settlement during the excavation of the second tunnel. That means the vertical deformation of the riverbed induced by the second tunnel excavation was negligible in the area above the centerline of the first tunnel, which is 15.2 m (~2.5 D) away from the centerline of the second tunnel. All sites show a slow gradual post-construction settlement with an average rate of approximately 3 to 5 mm/month with respect to the base. [PERSON] [47] observed that the settlement trough over a single tunnel could be represented within reasonable limits by a Gaussian distribution curve, which has become one of the simple and popularly used methods to predict soft ground settlements induced by shallow tunneling.