## 2 Zonal Rupture Modeling of Roadway Perimeter Rock under High Stress
### Base Range Modeling of Roadway Perimeter Rock Fragmentation Based on Discrete Element Approach
#### 2.2.1 Modeling  
The destruction process of the surrounding rock in the deep, high-stress soft rock roadway was adopted from the basic geological conditions of the belt transportation roadway in the mining area of the Quandian coal mine in Xuchang City, China. The section size of this roadway is 5.2 m \(\times\) 4.0 m, the burial depth is about 600 m, and the top and bottom plates of the rock formation consist of low-strength mudstone and sandy mudstone.  
Our model parameters were adopted from the data obtained from physical tests. As shown in Figure 4, the researcher collected core samples of the surrounding rock from the belt transportation roadway of the mining area at the Quandian coal mine. The uniaxial compressive test, the Brazilian splitting method tensile test, and the shear test were carried out on these samples using the MTS servo tester and the SYNS pressure shear machine, respectively. The mechanical parameters of the perimeter rock of this roadway were obtained as shown in Table 2.  
The deformation and fracture processes after roadway excavation were numerically simulated in this study by a model with a size of 80.0 m \(\times\) 64.0 m, as shown in Figure 5, which was realized via the commercial FLAC\({}^{\text{2D}}\) software package. The roadway vicinity was represented by a refined mesh with a size of 0.2 m \(\times\) 0.2 m.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Stratum** & **Densities, kg/m3** & **Bulk Modulus, GPa** & **Shear Modulus, GPa** & **Cohesion, MPa** & **Internal Friction Angle, \({}^{\circ}\)** \\ \hline Mudstone & 2300 & 1.2 & 0.3 & 1.0 & 16 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Test results of the mechanical parameters of the surrounding rock.  
Figure 4: Testing of mechanical parameters of surrounding rock: (**a**) test specimen; (**b**) servo testing machine; (**c**) shear tester; (**d**) uniaxial compressive test; (**e**) tensile test; and (**f**) shear test.  
In the simulations, we used a strain softening model for the reduction. The rock density was set at 2300 kg/m\({}^{3}\), while the bulk and shear moduli were set at 1.2 and 0.3 GPa, respectively. The strain softening model is a commonly used simulation method based on the Moore-Coulomb model that is not associated with the shear flow law but with the tensile flow law, the difference being that the cohesion, friction angle, shear expansion and dilatation, and tensile strength may change after the onset of plastic yielding. In the Moore-Coulomb model, such properties are assumed to remain constant. Users can define their own softening parameters, such as cohesion and friction angle, and set them as segmented linear functions (Figure 6). They can then use these softening parameters to measure plastic shear strains. In this model, we use data obtained from physical tests. This model calculates the total plastic shear and tensile strains by increasing the softening parameter at each time step and, in this way, drives the material properties to be consistent with the user-defined functions. For yield and potential functions, the plastic flow law and stress corrections are identical to the Moore-Coulomb model.  
Both vertical and horizontal in-situ stresses in the surrounding rock were set at 15.0 MPa. The horizontal displacement of both sides and the vertical displacement of the floor were fixed. The upper boundary was under a pressure of 15.0 MPa.