Effect of stress waveform on the rock blasting crack propagation mechanism using numerical simulation
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摘要: 運用RFPA3D動力分析軟件模擬了沖擊動力作用下含預制裂紋巖石的裂紋擴展過程，探究了應力波峰值、能量、上升及下降速率對巖石裂紋擴展過程的影響。研究表明動載下巖石裂紋擴展形態受應力波上升速率影響，應力波上升速率越快，孔周邊巖石越破碎；應力波能量影響裂紋擴展長度，能量越大裂紋擴展越長，而相同能量條件下，應力波上升速率越小，裂紋擴展距離越遠，但孔邊破碎程度越弱；上升速率和應力波上升沿能量共同影響著炮孔粉碎區半徑。數值模擬結果很好地揭示了不同應力波峰值、能量與上升/下降速率對巖石的破碎機制，在實際爆破作業中可以通過水炮泥封口或者采用空氣柱間隔裝藥結構來延長應力波作用時間，以達到擴大爆破影響范圍的目的，而通過選取合適類型與配比的炸藥來提升應力波上升速率從而增強孔邊破碎效果。Abstract: The type, proportion, and charging method of explosives produce different stress waveforms, which greatly affect rock crack propagation. Because of the complex interaction law between waveform parameters such as the peak value, wavelength, energy, and rise or fall rate, and the limited physical and mechanical test conditions, quantitatively controlling waveform parameters in a blasting test is difficult. Numerical simulation has advantages in revealing the influence law of the stress wave. In this paper, RFPA3D dynamic analysis software was used to simulate the crack propagation in a rock with a prefabricated crack under impact loads, and the effects of the stress wave peak value, energy, rise rate, and fall rate of the stress wave on the rock crack propagation process were investigated. Results show that the rock crack propagation pattern under dynamic loads was affected by the rise rate of the stress wave. The faster the stress wave rose, the more breakages occurred around the hole. For the crack propagation length, the crack grew longer with the increase in the stress wave energy. When the stress wave energy was constant, the crack grew farther with the decrease in the rise rate, but the broken degree around the hole was decreased. The rise rate and the energy of the rising edge of the stress wave affected the radius of the comminution zone. Numerical simulation results revealed the rock crushing mechanism of different stress wave peak values, energies, and rise or fall rates. In a practical engineering blasting operation, to expand the impact range of blasting, extending the action time using a water cannon mud seal or an air column interval charge structure was suggested. In addition, the appropriate type and proportion of explosives were also selected to increase the stress wave’s rise rate to improve the effect of hole edge crushing.
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Key words:
- explosive load /
- waveform /
- prefabricated crack /
- rock crack /
- three dimensional numerical simulation
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圖 3 荷載示意圖。 （a）H-1～H-6；（b）F-7～F-12；（c）S-13～S-17；（d）X-18～X-22；（e）N-23～N-27
Figure 3. Loads diagram: (a) H-1–H-6; (b) F-7–F-12; (c) S-13–S-17; (d) X-18–X-22; (e) N-23–N-27
圖 4 物理試驗與數值模擬結果對比圖。（a）物理試驗；（b）數值模擬
Figure 4. Comparison of (a) physical experiment and (b) numerical simulation
圖 5 荷載 H-3作用下模型最小主應力云圖。（a）20 μs；（b）30 μs；（c）40 μs；（d）60 μs；（e）80 μs；（f）120 μs
Figure 5. Minimum principal stress under load H-3: (a) 20 μs; (b) 30 μs; (c) 40 μs; (d) 60 μs; (e) 80 μs; (f) 120 μs
圖 6 右翼裂紋擴展尖端受力圖
Figure 6. Stress on the tip of the right wing crack propagation process
圖 7 不同波形應力波作用下的巖石裂紋擴展演化圖像
Figure 7. Rock crack propagation under different stress waveforms
圖 8 不同荷載作用下裂紋擴展細節分析。（a）H-2；（b）F-8；（c）H-5；（d）F-11
Figure 8. Crack growth analysis under different loads: (a) H-2; (b) F-8; (c) H-5; (d) F-11
圖 9 不同峰值應力波F-7~F-12（相同上升/下降速率）的裂紋擴展規律
Figure 9. Crack propagation with different peak stress waves F-7–F-12 (similar rise/fall rates)
圖 10 不同下降速率應力波X-18~X-22（相同上升速率）的裂紋擴展細節分析
Figure 10. Detailed analysis of the crack propagation of stress waves X-18–X-22 with different fall rates (similar rise rates)
圖 11 不同峰值作用下主裂紋擴展。（a）H-1~H-6；（b）F-7~F-12
Figure 11. Main crack propagation under different peaks: (a) H-1–H-6; (b) F-7–F-12
圖 12 模型累積損傷單元統計圖。（a）荷載S-13~S-17；（b）荷載X-18~X-22
Figure 12. Model cumulative damage unit statistics: (a) loads S-13–S-17; (b) loads X-18–X-22
圖 13 峰值應力波能量對裂紋擴展長度的影響。（a）主裂紋–峰值荷載；（b）右翼裂紋–峰值荷載；（c）不同峰值荷載的上升速率
Figure 13. Effect of the peak stress wave energy on the crack growth length: (a) main crack–peak loads; (b) right flank crack–peak loads; (c) rise rate of different peak loads
圖 14 速率應力波能量對裂紋擴展長度的影響。（a）主裂紋–速率荷載；（b）右翼裂紋–速率荷載；（c）不同速率荷載的上升速率
Figure 14. Effect of the rate of the stress wave energy on the crack growth length: (a) main crack–rate loads; (b) right flank crack–ate loads; (c) rise rate of different rate loads
圖 16 上升速率（a）和應力波上升沿能量（b）對粉碎區半徑的影響
Figure 16. Effect of the rise rate (a) and stress wave’s rising edge energy (b) on the radius of the crushing zone
表 1 材料參數
Table 1. Material parameters
Homogeneity index Elastic modulus / GPa Uniaxial compressive strength / MPa Density / (kg·m?3) Poisson ratio Friction angle / (°) 5 4.5 90 1120 0.25 30 
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