## 5 Drilling Pressure Relief Mechanism
### Borehole Mechanics Model Establishment and Pressure Relief Analysis
It is the elastic strain energy of rock mass (the unit is kJ/m\({}^{3}\)). Additionally, by substituting \(\sigma_{1}\) = \(\sigma_{2}\), \(\sigma_{3}\) = 0 into Equation (7), the following formula is obtained:  
Figure 13:1  
Substitute Formula (5) into Formula (8):  
Figure 13:2  
Substituting Equation (4) into Equation (9), we can find:  
Figure 13:3  
From Equation (2) minus Equation (3), the following formula is obtained:  
Figure 13:4  
Based on the definition of strain energy, it can be seen that at this time, the rock mass only considers the stress situation in the elastic range, and then \(\rho\) > r, and the substitution (11) has:  
Figure 13:5  
It can be seen that the stress value in the elastic zone is greater than the stress (\(\sigma_{r}\)) value at the elastic and plastic junction (here refers to the stress in the same direction), and it is easy to obtain the following relationship:  
Figure 13:6  
From Equations (4) and (10), it can be seen that the borehole radius \(R\) has a linear relationship with the radius \(r\) of the plastic zone around the borehole and has a quadratic relationship with the elastic strain energy stored in the rock mass. If the circular hole is regarded as a roadway, Formulas (3) and (4) show that when the radius \(R\) of the roadway and the confining pressure \(p\) are constant, the deeper the surrounding rock of the roadway is, the larger the radius \(r\) of the plastic region is, and the farther the stress peak goes into the deep surrounding rock, as shown in Figure 13:7 According to Formulas (9) and (13), the deeper the drilling depth, the larger the radius of the plastic zone around the hole (\(r\)), and the smaller the elastic strain energy stored in the rock mass. Combining Equations (10) and (13), it can be seen that if other conditions remain unchanged, the larger the borehole radius \(r\) is, the smaller the accumulated elastic strain energy of the rock mass is. The above discussions are all single-hole pressure relief, whereas, in actual engineering, multiple boreholes are used to relieve pressure together, so it is necessary to discuss the influence of borehole spacing on the pressure relief effect. Taking two boreholes with the same diameter and depth as an example, when the plastic zone formed between the boreholes begins to connect, the strain energy changes fastest and the pressure relief effect changes most obviously [9]. Based on this, in the case of the same diameter and depth of the two boreholes, the radius of the plastic zone of the single borehole is obtained, and then the maximum spacing between the plastic zones of the two boreholes is determined, as shown in Figure 16 (the stress is positive in tension and negative in compression). The parameter values measured by the non-porous test block are \(p=\sigma_{1}=\sigma_{c}=19.231\) MPa, the cohesion of the rock \(c=0.5\) MPa, and the internal friction angle \(\theta=27^{\circ}\). Substituting the measured parameter values into Equation (4) to calculate the radius of the single-hole plastic zone, \(r=4.286R\) m, and then the distance between the two boreholes should not be less than \(\Delta\)d = \(2r-2R=6.572R\). As the hole radius set by the borehole spacing in the laboratory test is \(R=0.5\) cm, it is calculated that when the spacing between the two boreholes \(3.286\) cm \(\geq\Delta\)d, the plastic zone around the hole is connected, and vice versa. In summary, construction drilling can unload the high stress in the rock mass and reduce the elastic strain energy stored in the rock mass, thereby achieving the effect of pressure relief. The larger the radius and depth of the borehole, the larger the radius of the plastic zone of the rock mass, and the smaller the strength of the rock mass and the cumulative elastic strain energy, the more the peak stress is transferred to the deep part, and the better the pressure relief effect, which is in line with the test conclusions of 2.1 and 2.2 in the text.