## 4 Numerical Analysis according to Tunnel Depth
### Analysis Conditions  
#### 4.1.1 Modelling and Applied Material Properties  
The target ground was modelled under the same stratum conditions as shown in Figure 2, and the ground of the GTX-A construction site, which comprised landfill, weathered soil, weathered rock, and hard rock layers, was modelled. In the previous numerical analysis, the boundary conditions of the X direction (both sides), Y direction (excavation direction), and Z direction (lower surface of ground modelling) of the model were set as quiet boundaries in the FLAC 3D program, so that the reflection wave in all directions were ineffective. For the blasting load, as shown in Figure 5, the same blasting pattern and blasting load as in the actual site were applied when the TBM and NATM parallel construction method was not used. The charge hole in the centre is perforated as shown in Figure 5. The number 1 and 2 in the figure mean different amounts of charge (A = 2.20 kg, B = 2.80 kg). Based on this, in order to compare the TBM and NATM parallel construction method and the use of protective shields, the NATM top surface excavation was simulated as shown in Figure 6. At this stage, the blasting pattern and blasting load were the same as those at the site, and only the size of the NATM tunnel was modelled according to the TBM and NATM parallel construction method. When the TBM and NATM parallel construction method was used, vibration-controlled blasting was considered, since the target ground is an urban area. Due to the condition of the TBM and NATM parallel construction method, expansion blasting was modelled with only outer shell holes excluding centre-cut blasting holes. The cross-section of the tunnel widened by NATM expansion blasting was 10.0 m, and the size of the pilot tunnel pre-excavated by TBM was 5.0 m (Figure 7). The mesh of each analysis used an automatically generated mesh by FLAC 3D. In this analysis, the ground and TBM material properties were calculated by referring to the GTX-A route ground survey report, and the ground and TBM were modelled using Mohr-Coulomb and elastic models, respectively. The applied material properties are listed in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Classification** & **Model** & \(\boldsymbol{\gamma}\) **(kN/m3)** & **E (kN/m2)** & \(\boldsymbol{\
u}\) & **c (kN/m2)** & \(\boldsymbol{\Phi}^{\prime}\) (\({}^{\circ}\)) \\ \hline Landfill & M-C & 18 & 13,000 & 0.3 & 0 & 31 \\ Weathered soil & M-C & 19 & 35,000 & 0.3 & 15 & 31 \\ Weathered rock & M-C & 20 & 300,000 & 0.3 & 30 & 33 \\ Hard rock & M-C & 27 & 12,900,000 & 0.2 & 1890 & 40 \\ TBM & Elastic & 78.5 & 20,000,000 & 0.2 & - & - \\ \hline \hline \end{tabular} \(\gamma\): Unit weight of soil, E: Young’s modulus, \(\
u\): Poisson’s ratio, \(c\): Cohesion, \(\Phi\): Angle of shearing resistance.  
\end{table}
Table 2: Ground and TBM material properties.  
Figure 5: Numerical modelling equivalent to field conditions.  
Figure 6: Top surface excavation numerical analysis modelling based on field conditions.  
Figure 7: Numerical analysis modelling of top surface excavation using TBM and NATM parallel construction method.