# Investigation on Cutting Blasting Efficiency of Hard Rock Tunnels under Different Charge Diameters
## 3 Numerical Simulation
### Simulated Results and Analysis
#### 3.3.2 Distribution Characteristics of the Stress Field  
In order to further understand the distribution features of the stress field in the cutting cavity under the three different charge diameters, the measurement points were arranged at the cutting depths of 2.5 m, 2.0 m, 1.5 m, 1.0 m, and 0.5 m in the center of the rock  
Figure 6: Stress wave propagation under the condition of \(\Phi\) 42 mm holes matching \(\Phi\) 35 mm cartridges. (**a**) Time = 160 \(\upmu\)s. (**b**)Time = 320 \(\upmu\)s. (**c**) Time = 470 \(\upmu\)s. (**d**) Time = 600 \(\upmu\)s.  
Figure 7: Stress wave propagation under the condition of \(\Phi\) 50 mm holes matching \(\Phi\) 42 mm cartridges. (**a**) Time = 160 \(\upmu\)s. (**b**)Time = 320 \(\upmu\)s. (**c**) Time = 470 \(\upmu\)s. (**d**) Time = 600 \(\upmu\)s.  
numerical model. Then, the stress-time curves of these measurement points were exported, as illustrated in Figure 8.  
Figure 8: Stress–time curves of measurement points. (a) \(\Phi\) 32 mm holes matching \(\Phi\) 27 mm cartridges. (b) \(\Phi\) 42 mm holes matching \(\Phi\) 35 mm cartridges. (c) \(\Phi\) 50 mm holes matching \(\Phi\) 45 mm cartridges.  
According to Figure 8, under working condition 1, of \(\Phi\) 32 mm blasting holes matching \(\Phi\) 27 mm cartridges, the peak stresses at the measurement points with cutting depths of 2.5 m, 2.0 m, 1.5 m, 1.0 m, and 0.5 m were equal to 94.3 MPa, 61.6 MPa, 35.7 MPa, 29.9 MPa, and 25.3 MPa, respectively. For working condition 2, of \(\Phi\) 42 mm blasting holes matching \(\Phi\) 35 mm cartridges, the peak stresses at the measurement points with cutting depths of 2.5 m, 2.0 m, 1.5 m, 1.0 m, and 0.5 m were equal to 133.8 MPa, 94.6 MPa, 54.7 MPa, 44.5 MPa, and 39.1 MPa, respectively. At the above corresponding measurement points, the peak stresses of the measurement points under condition 2 were 1.42, 1.54, 1.53, 1.49, and 1.54 times those under condition 1, which indicated that the blasting stress field intensity in the cutting cavity under condition 2 increased by 42-54% on the basis of condition 1.  
For working condition 3, of \(\Phi\) 50 mm blasting holes matching \(\Phi\) 42 mm cartridges, the peak stresses at the measurement points with cutting depths of 2.5 m, 2.0 m, 1.5 m, 1.0 m, and 0.5 m were equal to 186.4 MPa, 130.7 MPa, 78.6 MPa, 60.8 MPa, and 51.4 MPa, respectively. At the above corresponding measurement points, the peak stresses of the measurement points under condition 2 were 1.98, 2.12, 2.20, 2.03, and 2.03 times those under condition 1, and were 1.39, 1.38, 1.44, 1.37, and 1.32 times those under condition 2, respectively. The measurement results suggest that the stress field intensity in the cutting cavity under condition 3 was increased by 98-120% on the basis of condition 1, and increased by 32-44% on the basis of condition 2.  
Based on the above quantitative analysis, it was observed that the blasting stress field intensity in the cutting cavity could be significantly enhanced by increasing the charge diameter of the cutting holes. Predictably, the increase in the blasting stress field intensity was bound to enhance the destruction of the rock in the cutting cavity, which was conducive to forming small rock fragments that were easy to be discarded. Therefore, a cutting cavity satisfying the design cutting depth could be obtained in the hard rock underground tunnels.