## 2 Analysis of Rockburst Manifestation Characteristics
### Model Construction and Pressure Relief Scheme Design  
FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) is a finite-difference numerical modeling software widely used in geotechnical engineering for simulating the behavior of soil, rock, and structural support systems under various loading conditions. It is particularly suitable for analyzing nonlinear, plastic deformation and failure of rock masses. In this study, FLAC3D 5.0 was selected due to its robust ability to simulate complex stress redistributions and excavation-induced responses in underground mining environments.  
To effectively mitigate the risk of rockburst from the hard roof's caving during mining operations, the 21,103 operating face roadway of the Hulu Suyuan Coal Mine was chosen as a prototype. A three-dimensional numerical model was constructed using FLAC3D 5.0 with dimensions of 80 m (strike length), 20 m (dip width), and 45.18 m (vertical height).  
Based on field measurements, the buried depth of the operating face reached 640.82 m. The average rock density was 2500 kg/m\({}^{3}\), corresponding to an initial vertical stress of 16.02 MPa. The vertical stress signified the horizontal stress. The total number of elements in the model reached 576,000. The built-in Mohr-Coulomb constitutive model in FLAC3D was employed to simulate the nonlinear failure behavior of the rock mass. This study aims to investigate the impact of discrepant borehole inclination angles upon stress distribution in surrounding rocks, thus providing a theoretical basis for optimizing pressure relief parameters and guiding field implementation. Figure 6 displays the model's diagram.  
In Figure 2, the surrounding rock layers of the 21,103 working face roadway largely consist of medium-grained sandstone and sandy mudstone. According to the measured mechanical parameters of coal and rock strata, the parameters for each layer are calibrated as shown in Table 1.  
Based on laboratory physical simulation and ground pressure monitoring information, the roof's caving height in the 21,103 operating face ranges from approximately 11.3 to 21.2 m. Therefore, hydraulic fracturing boreholes must penetrate the main bearing section of the hard roof. The vertical depth of boreholes on the coal pillar should exceed 11 m. On the working face side, it should exceed 20 m to reach more than two-thirds of the hard roof thickness. Figure 7 and Table 2 illuminate the hydraulic fracturing pressure relief model and the nine numerical simulation schemes, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Rock Type** & **Thickness** & **Density** & **Bulk Modulus** & **Shear Modulus** & **Cohesion** & **Friction** & **Tensile Strength** \\  & **(m)** & **(kg/m\({}^{3}\))** & **(GPa)** & **(GPa)** & **(MPa)** & **Angle (\({}^{\circ}\))** & **(MPa)** \\ \hline Medium-grained & & & & & & & \\ Sandstone & 23.35 & \(2.42\times 10^{3}\) & 11.53 & 7.94 & 11.3 & 35 & 10.23 \\ Sandy Mudstone & 6.81 & \(2.59\times 10^{3}\) & 4.43 & 3.60 & 3.5 & 33 & 4.24 \\ No. 2-1 coal seam & 3.02 & \(1.26\times 10^{3}\) & 1.17 & 0.88 & 2.3 & 40 & 1.19 \\ Medium-grained & & & & & & & \\ Sandstone & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical parameters of numerical model.  
Figure 6: Numerical model of roof hydraulic fracturing pressure relief.