# Influence of Approaching Excavation on Adjacent Segments for Twin Tunnels
## 2 Case Studied Tunnels  
Twin tunnels have been built for the tunnel running from Caoqiao station to Fanjiacun station of metro line 10 in Beijing, China. A curved shield tunneling with a curvature radius of 840 m is prior to the second straight-line tunneling due to the restriction of site conditions. The plan view of twin tunnels of \(D=6\) m in close proximity to each other is shown in Figure 1a. During the approaching excavation, the distance between the two excavation faces along the route is larger than 200 m. The lateral spacing between the first tunnel and the second tunnel is gradually reduced to 2.7 m (less than \(D/2\), \(D\) is the external diameter of the tunnel) and then increases gradually as the second TBM shield advances away. Based on the geotechnical investigation report and the similar soil parameters adjacent to the existing project [25], the specific characteristics of the soil strata (Figure 1b) are summarized in Table 1. Friction angle and cohesion were obtained by direct shear tests. Young's modulus and Poisson ratio were obtained based on the standard triaxial tests and the similar soil parameters adjacent to the existing project [25]. Density was obtained by the cutting ring method.  
Figure 1: _Cont._  
Table 2 presents the specific specifications of the TBM shield as well as the circular segment consists of 5 regularly shaped blocks and a small-sized key block. The TBM shield utilized in this project is Herrenknecht shield machine (S-399), which belongs to earth pressure balance tunnel boring machines (EPB-TBM). The average advance rate and thrust force are 35 mm/min and 11.2 MN, respectively. The average rotation rate and torque of cutting wheel are 1.8 r/min and 3300 kN\(\cdot\)m, respectively. Especially, for the curved tunnel, the (double-sided) wedge-shaped segments were applied, the wedge magnitude and wedge angle of which are 48 mm and 0.46\({}^{\circ}\), respectively.  
In view of the particularity and complexity of the approaching excavation, the staged construction of the second straight-line tunnel will inevitably have an impact on the first curved tunnel, especially for the position of the minimum spacing between twin tunnels. To ensure the safety of the structure of the first tunnel, the vibrational chord strain gauges were arranged on the internal surface of the segment of the first tunnel at Cross-section B (Figure 1a), which hereafter is called the measured segment or measured cross-section. As shown in Figure 2, the monitoring strain gauges were set in the three positions (\(\alpha=0^{\circ}\), \(+45^{\circ}\), and \(-45^{\circ}\)), with each position existing two strain gauges that are oriented towards the circumference and axis, respectively. The initial frequency\(f_{0}\) was obtained when the distance from the measured cross-section to the second tunnel face is close to 100 m. Subsequently,  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Type of Soil**} & **Thickness** & **Young’s Modulus** & **Poisson Ratio** & **Cohesion (kPa)** & **Density (kN/m\({}^{3}\))** & **Friction Angle (\({}^{\circ}\))** \\ \hline Artificial fill & 1 & 18.5 & 0.25 & 16 & 16.5 & 12.2 \\ Sandy silt & 2.1 & 26 & 0.22 & 28 & 19.5 & 24.1 \\ Silty-fine sand & 2.7 & 35 & 0.26 & 0.2 & 20 & 26.8 \\ Round gravel & 6 & 45 & 0.3 & 0.3 & 20.5 & 35 \\ Sandy cobble & 38.2 & 130 & 0.18 & 0 & 21.5 & 40 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Soil properties.  
Figure 1: (a) Plan view of the project site; (b) Geological profile of Cross-section B.  
the monitoring frequency \(f_{\rm n}\) was recorded in real-time as the second tunnel advances. Then the strain increments \(\varepsilon\) can be estimated by:  
\[\varepsilon=k(f_{\rm n}-f_{0}), \tag{1}\]  
where \(k\) denotes the coefficient of the strain gauges calibrated before they are delivered.