# Numerical Study on the Pressure Relief Characteristics of a Large-Diameter Borehole
## 5 Analysis of the Pressure Relief Mechanism of the Large-Diameter Borehole  
According to the above research and analysis, after arranging large-diameter drilling holes in the roadway coal seam, the drilling holes are deformed and destroyed through the effect of the surrounding rock stress and spread around the coal body, with the drilling holes as the center. According to the degree of damage done to the coal body, they can be divided into the surrounding rock rupture area, plastic area, elastic area, and original rock area in turn, as shown in Figure 15. The larger the range of the coal fracture zone and plastic zone, the larger the range of the coal compaction, and the strength of the coal will decrease. After drilling the coal, stress concentration occurs on the borehole side, and the borehole shrinks to the borehole center under the effect of the internal stress of the coal, which will collapse when it exceeds the ultimate compressive strength of the borehole coal. The free space generated by drilling is filled by the collapsed coal; thus, drilling provides a compensation space for the surrounding rock deformation. The properties and occurrence conditions of the coal affect the range of the fracture zone and plastic zone of the coal. Referring to the previous research results [23], it is considered that, if the coal volume remains unchanged before and after the borehole collapse, the relationship between the radius \(R_{\text{b}}\) of the borehole rupture zone, the radius \(R_{0}\) of the borehole, and the radius \(R_{\text{b1}}\) of the final rupture zone can be obtained as follows:  
\[P\cdot\pi\Big{(}R_{\text{b}}^{2}-R_{0}^{2}\Big{)}=\ \pi R_{\text{b1}}^{2} \tag{4}\]  
In this formula, \(P\) is the coefficient of coal crushing and swelling in the cave-in area, and it is generally 1.2-1.5. According to the calculation, the radius of the fracture zone does not increase after drilling; that is, \(R_{\text{b1}}=R_{\text{b}}\). If the failure of the coal follows the Moore-Coulomb straight-line criterion, the final plastic zone radius \(R_{\text{P1}}\) can be obtained as follows:  
\[R_{\text{P1}}=R_{\text{b1}}\left(\frac{\left[\sigma_{\text{y}}(1+\lambda)+2c \cot\varphi\right](1\ -\sin\varphi)}{2c\cot\varphi}\right)^{\frac{1-\sin\theta}{2\sin\varphi}} \left(1+\frac{\sigma_{\text{y}}(1-\lambda)(1-\sin\theta\cos 2\theta)}{ \left[\sigma_{\text{y}}(1+\lambda)+2\cot\varphi\right]\sin\varphi}\ \right)n \tag{5}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Hole** & \multirow{2}{*}{\(X_{0}\)**/m**} & \multirow{2}{*}{\(L_{\text{SP}}\)**/m**} & **Hole** & \multirow{2}{*}{\(X_{0}\)**/m**} & \multirow{2}{*}{\(L_{\text{SP}}\)**/m**} \\
**Diameter** & & & & & \\ \hline
0.05 & 0.36 & 0.72–0.82 & 0.25 & 0.57 & 1.14–1.64 \\
0.10 & 0.47 & 0.94–1.14 & 0.30 & 0.61 & 1.22–1.82 \\
0.15 & 0.50 & 1.00–1.30 & 0.35 & 0.65 & 1.30–2.00 \\
0.20 & 0.53 & 1.06–1.46 & 0.40 & 0.71 & 1.42–2.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Reasonable borehole spacing under each hole diameter. Figure 15: Partition characteristics of the borehole coal body. In this formula, \(\sigma_{y}\) is the vertical stress, MPa; \(R_{\text{P}}\) is the radius of the plastic zone, m; \(\lambda\) is the lateral pressure coefficient; \(C\) is the coal cohesion, MPa; \(\varphi\) is the internal friction angle of coal, (\({}^{\circ}\)); \(\theta\) is the circumferential angle (\({}^{\circ}\)); and \(n\) is the correction coefficient, usually being 1.5-2.5. As shown in Figure 16, on the one hand, large-diameter drilling reduces the stress concentration of the coal; on the other hand, it changes the mechanical properties of the coal. After drilling, the surrounding rock mass is damaged, cracks develop, and the plasticity is enhanced. The plastic zones formed by multiple large-diameter drilling holes are connected, forming a wider range of plastic zones within the length of the drilling holes.