# Numerical Study on the Pressure Relief Characteristics of a Large-Diameter Borehole
## 4 Results
### Effects of the Hole Spacing on the Pressure Relief Effect
#### 4.3.4 Analysis of Reasonable Borehole Spacing  
From the above analysis of the stress, displacement, and plastic zone evolution characteristics between the boreholes, it can be seen that the main factor affecting the borehole pressure relief is hole diameter, and the secondary factor is the hole spacing. In the case of a certain borehole diameter, the borehole spacing has a great influence on the pressure relief effect of the coal. If the borehole spacing is too large, the pressure relief area of the coal cannot be connected, and the pressure relief effect is poor. If the borehole spacing is too small, the engineering quantity is great, and the cost is high. Therefore, it is necessary to determine the reasonable drilling spacing. In Figure 14, \(\gamma H\) is the original rock stress, where \(K_{1}\) and \(K_{2}\) are the stress concentration factors and \(K_{2}>K_{1}\), \(D\) is the diameter of the borehole, \(X_{0}\) is the radius of the plastic zone (the distance between the stress peak and borehole center), \(X_{1}\) is the width of the elastic zone between two boreholes, \(L_{\rm{In}}\) is the influence range of the borehole side stress, and \(L_{\rm{SP}}\) is the borehole spacing. Figure 13: Stress evolution between the boreholes with different hole diameters and hole spacings. As shown in Figure 14a, when \(L_{\text{SP}}\geq 2L_{\text{In}}\), the stress between boreholes showed a double peak shape, the coal between boreholes was not damaged, the plastic zone was not connected, the pressure relief effect was poor, and there was a risk of impact. As shown in Figure 14b, when \(1.5L_{\text{In}}\leq L_{\text{SP}}\leq 2L_{\text{In}}\), the stress between boreholes was saddle shaped, the coal between boreholes was still not damaged, the plastic zone was not connected, and the pressure relief effect was poor. With reference to the safety distance of the coal pillar in the roadway protection, the critical value of coal pillar safety is the width of the elastic core in the middle being \(2\;m\;(m\) is the mining height). However, pressure relief by drilling requires the man-made destruction of the rock mass; thus, the critical value of the coal mass destruction between drilling holes is \(2D\). Therefore, when \(L_{\text{SP}}=L_{\text{In}}+2D\) (as shown in Figure 14c), the coal between the boreholes was destroyed, the plastic zone was connected, and the pressure relief effect was good. When \(L_{\text{SP}}=L_{\text{In}}\), the stress between boreholes was a single peak, the plastic zones were connected, and the pressure relief effect was good. If the drilling spacing is reduced, the engineering quantity will increase, and the pressure relief cost will increase. To sum up, it is necessary to artificially destroy the coal between the boreholes and close the plastic zone during the pressure relief of the boreholes. Therefore, it is determined that the pore size range of the borehole in order to achieve good pressure relief is:  
\[L_{\text{In}}\leq L_{\text{SP}}\leq L_{\text{In}}+2D \tag{2}\]  
In this formula, \(L_{\text{In}}\) takes two times the radius of the plastic zone, namely \(L_{\text{In}}=2X_{0}\), to get:  
\[2X_{0}\leq L_{\text{SP}}\leq 2X_{0}+2D \tag{3}\]  
Through the numerical simulation experiment, the \(X_{0}\) value under each borehole diameter can be approximately obtained, and the reasonable borehole spacing under different borehole diameters can be calculated by substituting Equation (5). The calculation results are shown in Table 2.  
To sum up, the main factor affecting the pressure relief effect of the drilling is the diameter of the drilling holes, and the secondary factor is the spacing of drilling holes. Therefore, when drilling machine tools allow, the hole diameter should be increased first, and then the reasonable hole spacing should be selected, so as to minimize the amount of pressure relief at work. Figure 14: Analysis model of reasonable borehole spacing. (**a**) \(L_{\text{SP}}\geq 2L_{\text{In}}\). (**b**) \(L_{\text{SP}}\geq 2L_{\text{In}}\).