## 3 Deformation and Failure Characteristics of Surrounding Rock of Roadway
### Analysis of Stress Concentration Area in Roadway  
In this section, we will analyze the stress distribution characteristics of the 1211, 10,209, and 1411 working faces of Zhongxing Coal Industry after the mining process. We will use three-dimensional numerical software (Version 5.0, Itasca Consulting, Inc., USA)to examine these characteristics. The model consists mainly of displacement boundaries and stress boundaries. The stress boundary represents the gravitational forces of the rock layers that are not included in the simulated roof rock layer. The displacement boundary is defined as X = 0, 500 m, Y = 0, 400 m, and Z = 50. These boundaries are specified as fixed displacement bounds. Additionally, the top of the model will have a downward vertical tension of 7.82 MPa applied to it, based on calculations. To simplify the geological circumstances of the site, the size of the three-dimensional numerical model is established as length \(\times\) width \(\times\) height = 500 m \(\times\) 400 m \(\times\) 290 m. The size of the working face of the model 1409 airway is shown as width \(\times\) height = 4200 mm \(\times\) 2400 mm in Figure 7. The model consists of 1,695,456 nodes and 1,590,625 units. By incorporating the displacement boundary and stress boundary conditions with other elements, we can determine the boundary settings of the numerical model. The schematic of the numerical model is presented in Figure 8.  
Figure 7: Numerical model location relationships and boundary conditions. Because rock is an elastic-plastic material, the Mohr-Coulomb criterion for the ideal elastoplastic body is used to judge the deformation and failure of rock. \[f_{\mathrm{s}}=\sigma_{1}-\sigma_{3}\frac{1+\sin\varphi}{1-\sin\varphi}+2c\sqrt{ \frac{1+\sin\varphi}{1-\sin\varphi}}. \tag{1}\]  
In this formula, \(\sigma_{1}\) and \(\sigma_{3}\) are the maximum and minimum principal stress, respectively, \(c\) is the adhesive force, and \(\varphi\) is the friction angle. When \(f_{\mathrm{s}}>0\), the material will undergo shear failure and strain softening. Under normal stress conditions, the tensile strength of the rock mass is very low; thus, one can judge whether the rock mass has tensile failure according to the tensile strength criterion (\(\sigma_{3}\geq\sigma_{T}\)). Table 2 displays the numerical simulation's rock strata parameters. The physical and mechanical properties of the coal rock are used to perform experimental measurements on the numerical simulation parameters. To monitor changes in stress, we will excavate working faces 1211, 1411, and 10,209. By analyzing the records, we can determine the distribution of vertical stress in the hollow area created by mining these faces. We will also study the changes in lateral stress in the coal pillar of the 1409 airway. Along the edge of the 1411 extraction zone, we will place stress monitoring points every 3 m. The measuring line will be 36 m long, and we will use FLAC's histogram command flow to record the stress values at the monitoring points. Figure 9 shows the stress distribution features of airway 1409 during the excavation of working faces 1211, 10,209, and 1411. After mining these faces, both the vertical and horizontal strains increase. There are two zones of stress rise, with peak values of 29.9 MPa and 25.2 MPa, respectively, along the side of the coal pillar of the working face. These zones are 18 m apart. At a distance of 28 m from the coal pillar side, there are 1409 airways that experience stress. Sections I and II of the 1409 airway have high-stress zones due to the combined horizontal and vertical stresses in the stress rise zone.