## 5 Numerical Modeling
### Results of the Numerical Study and Discussion
#### 5.3.5 Impact of the Step Length in the Construction of the Pilot Tunnels  
Different step lengths of 1 m, 2 m, 3 m, 4 m and 5 m were selected to investigate the impact of the excavation step length on the stability of the excavation face, and also on the final surface settlement and crown settlement. The height of each step is half of the pilot tunnel diameter.  
(1) Stability analysis of excavation face  
The stability of the excavation face must be considered in tunnel construction. Pilot construction supported by STS structure is different from other arching excavation face. Considering the bottom tunnel pilots (Z1 and Z3) satisfy the symmetry, the tunnel pilot (Z1) is listed as an example to investigate the stability of top pilot tunnel in this section.  
The horizontal displacement of the excavation face in the pilot tunnel Z1 is shown in Figure 33. When the step length is 3 m, the maximum horizontal displacement is 3.4 mm which occurs slightly lower than the center of the upper step section. The displacements decrease gradually with the increase of step length. When the step length is larger than 3 m, the step length has a little effect on the displacement of the excavation face. The numerical results indicate that sliding between upper and lower steps may happen when the step length is less than 3 m. The numerical results highlight the importance of adopting an appropriate step length in the stability of the excavation face. Based on the results of the numerical analysis, it seems that one tunnel diameter, which is 3 m in the case of this simulation, is appropriate for this purpose. Although larger step lengths will also have similar face displacements, they may result in larger ground settlement due to the delay they cause in installation of the initial supports of the tunnel.  
Figure 33: Horizontal displacement at the tunnel face for different step lengths.  
Figure 32: Longitudinal deformation curve: (**a**) Ground longitudinal settlement; (**b**) Longitudinal deformation of horizontal STS structure.  
2. Ground Settlement Monitoring points were installed on the crown of the pilot tunnel Z1 in longitudinal direction at y = 20 m in order to investigate the impact of step length on ground settlement.  
In this section, the effect of different step lengths on the ground settlement and crown settlement at cross section with y = 20 m is investigated through the numerical simulations, and the ground settlement profile and crown settlement profile are showed in Figures 34 and 35.  
As seen from Figures 33 and 34, the step length has great influence on the ground and tunnel crown settlement above the excavation face. The ground settlement increases with the increase of step length. This is because when the step length is large, it is hard to effectively control the settlement because the ring supports can only be installed when both steps of the excavation are completed. The small local heaves observed in the ground settlement profiles are mainly due to the negative moment created at the end of the horizontal section of the STS system due to settlements of the middle section of the STS system. As shown in Figure 35, larger stage length can cause more crown settlement, appropriate step length must be selected so that the support rings can be quickly installed and the ground settlements can be controlled.