Impact-Induced Fracture Process and Energy Dissipation Characteristics of Copper-Bearing Albite Rock Based on FDEM
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摘要: 为了保证铜矿资源的高效回采，以含铜钠长岩试样为研究对象，使用分离式霍普金森压杆施加不同强度的冲击荷载，利用高速摄像系统记录裂纹扩展过程，并结合一维应力波传播理论和能量守恒定律，分析试样在不同冲击气压下的能量耗散规律；同时，基于有限-离散元耦合算法，建立含铜钠长岩冲击过程的数值模型。结果表明：入射能和应力峰值随着冲击气压的增大而增大，试样破碎程度也随之加剧；当入射能小于140 J时，随着入射能的增大，能量耗散率逐渐增大；当入射能大于140 J时，能量耗散率随入射能的增加逐渐减小，能量耗散率在冲击气压为0.35 MPa时最大；在冲击过程中，拉伸破坏占主导作用，并在水平方向形成主优势区。新增裂纹面积和冲击总能量随着冲击荷载的增加而增大；冲击气压为0.30 MPa时，应变能比能量最小，在此气压下，剪切裂纹占比最小，说明0.30 MPa冲击气压的破岩效率最高；基于有限-离散元构建的数值模型可以有效预测在不同冲击荷载下含铜钠长岩的损伤破裂过程。Abstract: In order to ensure the efficient recovery of copper resources, the copper-bearing albite rock samples were taken as the research object, and the impact loads with different strengths were applied by the split Hopkinson pressure bar (SHPB). The crack propagation process was recorded by a high-speed camera system, and the energy dissipation law of the samples under different impact pressures was analyzed by combining the one-dimensional stress wave propagation theory and the law of conservation of energy. At the same time, a numerical model of the impact process of copper-bearing albite is established based on the finite-discrete element coupling algorithm. The results show that the incident energy and the peak stress increase with the increase of the impact gas pressure, and the degree of sample breakage also increases. When the incident energy is less than 140 J, the energy dissipation rate increases with the increase of the incident energy. When the incident energy is greater than 140 J, the energy dissipation rate decreases with the increase of the incident energy, and the energy dissipation rate reaches the maximum when the impact gas pressure is 0.35 MPa. In the process of impact, tensile failure plays a dominant role and forms the main dominant area in the horizontal direction. The new crack area and the total impact energy increase with the increase of impact load. When the impact gas pressure is 0.30 MPa, the strain energy ratio is the smallest. Under this pressure, the proportion of shear cracks is the smallest, indicating that the rock breaking efficiency of 0.30 MPa impact gas pressure is the highest. The numerical model based on finite-discrete element method can effectively predict the damage and fracture process of copper-bearing albite under different impact loads.
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图 5 不同冲击气压下含铜钠长岩的裂纹演化过程
Figure 5. Crack evolution process of copper-bearing albite under different impact gas pressures
图 6 不同冲击气压下含铜钠长岩的破碎形态
Figure 6. Fracture morphology of copper-bearing albite under different impact gas pressures
图 9 实验室测试与模拟结果对比
Figure 9. Comparison between laboratory tests and numerical simulation results
图 10 含铜钠长岩试样数值计算模型
Figure 10. Numerical model for the copper-bearing albite rock sample
图 11 不同冲击气压下模型的裂纹演化（蓝色代表拉伸裂纹，红色代表剪切裂纹）
Figure 11. Crack propagation in the model under different impact gas pressures (Blue denotes tensile cracks, red denotes shear cracks.)
图 12 不同冲击气压下含铜钠长岩试样的裂纹数和AE计数（蓝色代表拉伸裂纹，红色代表剪切裂纹）
Figure 12. Crack number and AE count of copper-bearing albite rock samples under different impact gas pressures (Blue denotes tensile cracks, red denotes shear cracks.)
图 13 不同冲击气压下含铜钠长岩裂纹走向玫瑰图（蓝色代表拉伸裂纹，红色代表剪切裂纹）
Figure 13. Rose diagrams showing fracture orientation distributions under different impact gas pressures (Blue denotes tensile cracks, red denotes shear cracks.)
图 14 冲击气压、比能量、新增裂隙面积的关系
Figure 14. Relationships among impact gas pressure, specific energy, and newly created fracture area
表 1 含铜钠长岩基本物理力学参数
Table 1. Basic physical and mechanical properties of copper-bearing albite rock
ρ/(g·cm−3) Longitudinal wave velocity/(m·s–1) E/GPa $\nu $ Compressive strength/MPa 2.857 3384 76.25 0.46 37.61 
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表 2 含铜钠长岩的冲击试验数据
Table 2. Impact test results on copper-bearing albite rock
Test No. Impact pressure/MPa Impact velocity/(m·s–1) Average strain rate/s−1 Peak stress/MPa HT-1 0.25 5.34 41.55 97.76 HT-2 0.30 6.76 56.23 117.59 HT-3 0.35 8.32 61.14 133.15 HT-4 0.40 10.27 71.16 136.93 HT-5 0.45 12.81 81.39 161.88
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表 3 不同冲击气压下含铜钠长岩能量计算
Table 3. Energy analysis of copper-bearing albite during impact under different gas pressures
Test No. Average strain rate/s−1 Impact gas pressure/MPa WI/J WR/J WT/J WD/J HT-1 41.55 0.25 64.52 20.92 24.95 18.64 HT-2 56.23 0.30 94.97 24.03 40.05 30.89 HT-3 61.14 0.35 136.95 36.02 51.10 49.83 HT-4 71.16 0.40 156.82 45.00 56.96 54.85 HT-5 81.39 0.45 196.28 59.74 58.75 61.47
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表 4 FDEM微观参数
Table 4. Calibrated micro-mechanical parameters for the FDEM model
r/(kg·m–3) E/GPa $\nu $ pn/GPa pt/GPa c/MPa j/(°) ft/MPa GfⅠ/(J·m–2) GfⅡ/(J·m–2) pfn/GPa pft/GPa 2857 76.25 0.46 76.25 76.25 6.29 53.03 4.21 1000 2000 7625 7625
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