Blasting Crater Test Law under Different Resistance Lines Based on DEM-PBM Method
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摘要: 在露天爆破中，最小抵抗线决定了爆破能量释放的主导方向和岩石运动速度的方向，是控制爆破作用范围、岩石破碎效果及抛掷路径的核心因素。基于DEM-PBM（discrete element method-population balance model）耦合的爆破漏斗数值模拟方法，通过多尺度建模与试验数据协同分析，结合现场爆破漏斗试验，对不同最小抵抗线下爆破漏斗破岩规律进行了研究，以优化爆破参数，提高爆破效率和安全性。数值模拟结果表明：当抵抗线长度为1.05 m时，20 ms时的爆破扩腔面积比5 ms时增长70.33%；当抵抗线长度为1.85 m时，爆破扩腔面积增长11.42%。对比不同抵抗线下破碎块度的抛掷作用效果，当抵抗线长度为1.05 m时，抛掷效果最佳。现场爆破漏斗试验结果显示：当抵抗线长度增大时，爆破漏斗体积变小；当抵抗线长度为1.05 m时，爆破漏斗体积最大，与数值模拟得到的爆破扩腔规律相似。现场爆破块度尺寸分形规律分析结果表明，当抵抗线长度为1.05 m、炮孔深度为1.2 m时，抛掷岩石块体较多，块度分布适中，破碎块体抛掷作用效果最佳。研究结果可为现场钻爆参数优化提供一定参考。Abstract: In open-pit blasting project, the minimum resistance line (W) determines the dominant direction of blasting energy release and the maximum direction of rock velocity. This parameter is the core factor controlling the blasting action range, crushing effect and throwing path of the rock. Based on discrete element method-population balance model (DEM-PBM) coupling numerical simulation method of blasting crater, field blasting crater test was carried out through multi-scale modeling and test data collaborative analysis. The rock breaking law of blasting crater test under different minimum resistance lines was studied in order to optimize blasting parameters and improve blasting efficiency and safety. Based on the comparison of numerical simulation results, the blasting expansion area at 20 ms increases by 70.33% compared with that at 5 ms when W=1.05 m, and the blasting expansion area increases by 11.42% when W=1.85 m. By comparing the throwing effect of fragmentation under different minimum resistance lines, the throwing effect is the best when W=1.05 m. According to the results of field blasting crater test, when the length of the resistance line increases, the volume of the blasting crater becomes smaller, and the volume of the blasting crater is the largest when W=1.05 m, which is similar to the blasting cavity expansion law obtained through numerical simulation. The fractal law of fragmentation size in field blasting was analyzed. When W=1.05 m and the depth of blast hole is 1.2 m, more rock blocks are thrown, the fragmentation distribution is moderate, and the throwing effect of broken blocks is the best. This study provides reference for the optimization of field drilling and blasting parameters.
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Key words:
- DEM-PBM method /
- blasting crater /
- throwing action /
- blasting fragmentation
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图 7 不同抵抗线下岩石的累积损伤云图
Figure 7. Cumulative damage nephogram of rock under different resistance lines
图 8 不同时刻、不同抵抗线长度下爆腔切片面积
Figure 8. Section area of explosive chamber at different time under different resistance lines
表 1 不同最小抵抗线参数
Table 1. Parameters of different minimum resistance lines
No. Aperture/cm Charge diameter/cm Hole depth/m Charge mass/kg Charge height/cm Minimum resistance
line length/m1 15 8.6 1.2 2.1 30 1.05 2 1.4 1.25 3 1.6 1.45 4 1.8 1.65 5 2.0 1.85 
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表 2 磷矿石的HJC本构参数
Table 2. HJC constitutive parameters of phosphate ore
ρ0/(kg·m−3) G/GPa A B C N fc/MPa 2 415 47.2 0.053 8 2.321 47 0.024 9 0.783 37 118 T/MPa pc/MPa ρl/(kg·m−3) K1/GPa K2/GPa K3/GPa 6.78 39.33 2 444.33 12 8.64 69.98
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表 3 炸药的相关参数
Table 3. Relevant parameters of explosives
Dt2/cm L/cm m/kg D0/(m·s−1) Explosive force value/mL Ferocity/mm Burst distance/cm 3.2 30 0.3 4500 320 16 4
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表 4 爆破漏斗半径
Table 4. Blasting crater radius
W/m r/m 1.05 0.934 1.25 0.851 1.45 0.382 1.65 0.215 1.85 0.034
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表 5 现场试验数据
Table 5. Field test data
No. Hole depth/m Resistance line length/m Funnel depth/m Funnel radius/m Funnel volume/m³ 1 1.2 1.05 0.931 0.934 1.043 2 1.4 1.25 0.851 0.851 0.947 3 1.6 1.45 0.421 0.382 0.269 4 1.8 1.65 0.334 0.215 0.193 5 2.0 1.85 0.230 0.034 0.105
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表 6 不同抵抗线长度下的平均块度分布
Table 6. Average block size distribution under different resistance lines
W/m d50/cm 1.05 28 1.25 36 1.45 22 1.65 34 1.85 35
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