## 4 Numerical Simulation of Excavation and Support
### Numerical Model and Calculation Parameters  
Taking the tunnel and rock mass as the research object, the model was established, and the Mohr-Coulomb model was selected as the constitutive model. The horizontal and vertical directions of the model are 80 m (about 10 times the diameter of the tunnel), and the mesh of the three-dimensional model is divided into 44,580 elements and 48,007 nodes, as shown in Figure 4. The buried depth of the tunnel is 300 m, which makes it a deep-buried tunnel. Unlike shallow burial, terrain changes have little effect on the tunnel excavation. The initial in situ stress was applied according to the buried depth and the fixed displacement method was used for simulation. The normal displacement constraints were applied to the side and bottom of the numerical model, and the top was the free surface.  
Figure 3: (**a**) Variation curve of radius of plastic zone with support resistance; (**b**) Variation curve of peripheral displacement with support resistance.  
The rock mass of the diversion tunnel is dominated by phyllite. Based on the detailed geological exploration report, relevant codes and engineering analogy of the Dongsong Hydropower Station, the calculation parameters of the rock mass were selected as shown in Table 1. The design and excavation section of the main diversion tunnel is horseshoe-shaped. The arch frame support is made of 18 I-steel with a longitudinal spacing of 100 cm. The bolt support adopts a mortar bolt with a length of 4.5 m and spacing of 1.5 \(\times\) 1 m. Feet-lock bolts are constructed at the arch foot. Initial support is made of shotcrete with a strength of C20 (the standard strength of concrete is 20 MPa) and thickness of 20 cm. The spacing of the welded steel mesh is 15 cm (@ 15 \(\times\) 15).  
The second lining is made of mold casting concrete with a strength of C30 and thickness of 60 cm.  
Rock mass was simulated by a solid element, arch support was simulated by a beam element, bolt support was simulated by a cable element, and concrete was simulated by a shell element. Welded steel mesh was not simulated separately, which was achieved by equivalent improvement of shotcrete parameters. The physical parameters of each supporting structure in practical engineering are shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Parameter** & **Severity (KN/m3)** & **Passion’s Ratio** & **Eastic Modulus (GPa)** & **Cohesion (MPa)** \\ \hline Steel arch frame & 82 & 0.29 & 185 & - \\ Bolt & 80 & 0.3 & 170 & 0.02 \\ Shotcrete & 23 & 0.2 & 21 & - \\ Mold casting concrete & 25 & 0.2 & 30 & - \\ \hline \end{tabular}
\end{table}
Table 2: Calculation parameters of the supporting structure.  
Figure 4: Three-dimensional meshed model of numerical calculation.  
In the simulation, the two-bench method scheme was adopted according to the actual construction. The upper and lower benches were excavated at the same time, and the excavation footages were kept unchanged. The excavation footage was 1 m per cyclic step, and initial support was constructed immediately after the excavation was completed. Assuming that initial support is in close contact with the rock mass, the buried depth of the tunnel was 300 m, and the lateral pressure coefficient was 1.0.