# Influence of Approaching Excavation on Adjacent Segments for Twin Tunnels
## 5 Optimization of Construction Schemes
### Internal Forces in the Segment  
Figure 15 shows the variations of internal forces in the measured segment of the first tunnel in two construction cases. The profiles of normal force and bending moment in these two cases are asymmetric with respect to the tunnel axis. The peak values of internal forces occur at the regions near the second tunnel. As seen in Figure 15a, the peak value of normal force in case II (\(\alpha=180^{\circ}\)) is about 189 kN/m larger than that in case I (\(\alpha=0^{\circ}\)). As seen in Figure 15b, the peak value of the negative  
Figure 14: Comparisons of ground displacements in two construction cases: (**a**) ground surface settlement; and (**b**) horizontal ground displacement.  
bending moment in case II (\(\alpha=165^{\circ}\)) is about 9 kN\(\cdot\)m/m larger than that in case I (\(\alpha=345^{\circ}\)); The peak value of the positive bending moment in case II (\(\alpha=90^{\circ}\)) is about 17 kN\(\cdot\)m/m larger than that in case I (\(\alpha=75^{\circ}\)).  
Furthermore, the safety factors of the concrete member are introduced to make a comparison of the construction schemes [47]. If the eccentricity \(e_{0}\) of a rectangular concrete member is less than one-fifth of its thickness \(h\) (i.e., \(e_{0}\leq 0.2h\)), the bearing capacity of the concrete member is controlled by its compressive strength. If \(e_{0}>0.2h\), the bearing capacity is controlled by its tensile strength. Then the safety factors (\(K_{c}\) or \(K_{t}\)) can be estimated by:  
\[\left.\begin{array}{l}K_{c}\ =\ \frac{\beta_{1}\beta_{2}K_{b}h_{1}h}{N},\ (e_{0}\leq 0.2h),\\ K_{t}\ =\ \frac{1.75\beta_{1}R_{b}h_{1}h}{N(6e_{0}/h-1)},\ (e_{0}>0.2h)\end{array}\right\} \tag{3}\]  
where \(\beta_{1}\) and \(\beta_{2}\) denote the buckling and acentric coefficients, respectively, \(R_{c}\) and \(R_{t}\) denote the ultimate compressive and tensile strengths of concrete, respectively, and \(b_{1}\) denotes the width of the member. Specifically, \(e_{0}\) is the ratio of bending moment (M) to normal force (N) calculated above, \(h=0.4\) m, \(\beta_{1}=1\), \(R_{c}=36.5\) MPa, \(R_{t}=3.1\) MPa, \(b_{1}=1\) m, while \(\beta_{2}\) can be calculated by:  
\[\beta_{2}\ =\ 1+0.648\frac{e_{0}}{h}-12.569(\frac{e_{0}}{h})^{2}+15.444(\frac{e _{0}}{h})^{3} \tag{4}\]  
The safety factors for the two construction cases are obtained by Equations (2) and (3). As shown in Figure 16, the distribution of safety factors along the periphery in case I can effectively cover the results in case II. Moreover, the minimum safety factor in case I (13.6) is larger than that in case II (6.0), which indicates that the concrete member in case I is safer.  
In general, the selection of a reasonable construction scheme requires the integrated consideration of the influence of approaching excavation on the displacements of the surrounding environment and the internal forces of the tunnel structure. If the case I is selected, it will result in smaller internal forces of the segment. If the case II is selected, it will result in a smaller horizontal displacement of the ground between twin tunnels. In actual construction, the case I is selected as the implementation scheme.  
From the perspective of effectively controlling the vertical displacement of the ground and the internal forces of the tunnel structure, this decision is relatively reasonable. Note that the construction loadings should be reasonably controlled to prevent excessive horizontal displacements.  
Figure 15: Comparisons of internal forces in the measured segment of the first tunnel: (**a**) normal force; and (**b**) bending moment.