# Numerical Study on the Pressure Relief Characteristics of a Large-Diameter Borehole
## 4 Results
### Effects of the Hole Diameter on the Pressure Relief Effect
#### 4.1.2 Strain Energy Density Evolution Law  
From the strain energy density, the influence of the drilling hole diameter on the energy release effect was analyzed. The experimental results are shown in Figure 6. From Figure 6a, it can be seen that when the hole diameter was 0.05 m, the strain energy density of the coal body on the drilling side of the roadway was basically unchanged, the energy core still existed, and the accumulated energy in the coal body was not released. When the hole diameter was 0.10 m to 0.40 m, the energy core in the coal on the side of the borehole disappeared, and the energy -releasing area of the coal around the borehole gradually increased with the increase in the hole diameter. In Figure 6b, \(L_{\mathrm{P}}\) indicates the peak position of the original strain energy density, \(L_{\mathrm{P1}}\) indicates the peak shift position of the strain energy density after drilling, and \(E_{0}\) indicates the strain energy density in the original rock area. It can be seen from Figure 6b that, after drilling, the peak value of the strain energy density decreased and moved to the deep area. When the hole diameter was 0.05 m, the strain energy density decreased a little, and the energy release effect was poor. When the hole diameter was 0.10 m to 0.40 m, the strain energy density in the coal decreased uniformly with the increase in the hole diameter, and the energy release effect gradually improved.  
The strain energy density \(E_{0}\) = 37.32 KJ/m\({}^{3}\) in the deep rock area of the roadway, with \((E_{\mathrm{P}}-E_{0})/E_{0}\) (where \(E_{\mathrm{P}}\) is the peak value of the strain energy density and \(E_{0}\) is the strain energy density in the original rock area), was used as the representative value of the energy release effect of the borehole. A positive value indicated energy accumulation and a negative value indicated energy release, as shown in Figure 7.  
\((E_{\mathrm{P}}-E_{0})/E_{0}\) gradually decreased with the increase in the hole diameter, which indicates that the energy accumulation in the coal on the borehole side decreased with the increase in the hole diameter. When the hole diameter was \(D\geq\) 0.20 m, \((E_{\mathrm{P}}-E_{0})/E_{0}<0\), there was no energy accumulation in the original rock area, which indicates that the elastic energy accumulation in the coal throughout the whole borehole length was small at this time. Increasing the hole diameter only led to the decrease in the strain energy density in the borehole range, which indicates that the energy release effect of the borehole was further enhanced with the increase in the hole diameter.  
Figure 6: Energy release characteristics of the large-diameter borehole with different hole diameters. (**a**) Evolution characteristics of the strain energy contour plot with different diameters. (**b**) Evolution characteristics of the strain energy density curves with different diameters.  
By analyzing the evolution law of stress and strain energy density under different diameters of the large-diameter borehole, it can be concluded that the peak values of stress and strain energy density, after drilling, decreased and moved to the deep area. With the increase in the borehole diameter, the stress concentration and strain energy density in borehole coal decreased, and the pressure relief area gradually increased. There was basically no pressure relief when the hole diameter was too small; thus, a reasonable hole diameter is 0.10 m\(\sim\)0.40 m, according to the actual situation (the mechanical properties of coal and rock, the diameter of existing drilling rig in the mine, etc.).