## 4 Numerical Calculations
### Results
#### 4.3.2 Plasticity State of the Surrounding Rock  
In FLAC\({}^{\text{3D}}\), a conventional Mohr-Coulomb plasticity state indicates two types of failure mechanisms: shear and tensile. A distinct hue represents each category. The graph also shows whether stresses inside a zone are on the yield surface (the zone is currently at active failure, -n), or whether the zone failed earlier in the model run, but the stresses have now fallen below the yield surface (the zone has failed in the past, -p). Although initial plastic flow may occur at the start of a simulation, further stress redistribution unloads the yielding components, causing their stresses to no longer fulfill the yield requirement, as shown by shear-p or tension-p.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Lithology**} & **Tensile Strength** & **Elasticity** & **Poisson** & **Density** & **Cohesion** & **Friction** \\  & **(MPa)** & **(Gpa)** & **Ratio** & **(kg/m\({}^{\text{3}}\))** & **(MPa)** & **Angle (\({}^{\text{c}}\))** \\ \hline Sandy & 3.90 & 34.4 & 0.26 & 2535 & 19.10 & 30 \\ mudstone & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mechanical properties used in the Mohr–Coulomb model.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
\begin{tabular}{c} Plastic Shear \\ Strain \\ \end{tabular} & 0 & \(1\times 10^{-3}\) & \(5\times 10^{-3}\) & \(1\times 10^{-2}\) & 1 \\ \hline Cohesion & 0.5 & 0.3 & 0.2 & 0.1 & 0.5 \\ \hline Tensile & & & & & \\ Strength & 0.3 & 0.2 & 0.1 & 0.05 & 0.1 \\ (MPa) & & & & & \\ \hline Friction & 28 & 25 & 22 & 19 & 19 \\ Angle (\({}^{\text{c}}\)) & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mechanical properties used in the strain-softening Mohr–Coulomb model.  
Figure 5: Stress distribution in the surrounding rock. (**a**) Vertical stress distribution (MPa); (**b**) Vertical stress concentration factor distribution; (**c**) Horizontal distribution (MPa); (**d**) Horizontal stress concentration factor distribution.  
Figure 6: (**a**) Characteristics of vertical stress on monitoring line A-A\({}^{\prime}\) (Figure 5) with calculation steps; (**b**) Characteristics of horizontal stress on monitoring line B-B\({}^{\prime}\) (Figure 5) with calculation steps.  
With an increase in the number of calculation steps in each cycle, both the ratios of the shear and tension failure volumes of the surrounding rock to the excavated volume of the roadway change (Figure 7). Simultaneously, the expansion of the roadway plastic zone was also reflected. After the excavation of the roadway, shear failure occurred mainly in the surrounding rock and tension failure occurred on the floor of the roadway. From the curve in Figure 7, it was observed that in the initial stage of tunnel excavation, shear failure mainly occurs on the roof and floor, and the degree of damage of the floor is larger than that of the roof. With an increase in the number of calculation steps, the volume of shear failure increases linearly, and the tensile failure volume fluctuates. The tensile failure concentrates on the floor due to the gradual failure of the supporting system and the decline in the bearing capacity of the surrounding rock. Because the floor is not supported, the concentrated stress is released from it, causing dilation damage to the floor. Therefore, along with strengthening the support of the sides and roof, the floor should also be strengthened.