冲击荷载下含铜矿岩能量耗散的数值模拟

左庭; 李祥龙; 王建国; 胡启文; 陶子豪; 胡涛; 章彬彬; 宋家旺

doi:10.11883/bzycj-2024-0214

冲击荷载下含铜矿岩能量耗散的数值模拟

doi: 10.11883/bzycj-2024-0214

左庭^{1, 2,},
李祥龙^{1, 2, ,},
王建国^{1, 2},
胡启文^{1, 2},
陶子豪^{1, 2},
胡涛^{1, 2},
章彬彬³,
宋家旺⁴

1.
昆明理工大学国土资源工程学院，云南昆明 650093
2.
云南省教育厅爆破新技术工程研究中心，云南昆明 650093
3.
核工业井巷建设集团有限公司，浙江湖州 313000
4.
内蒙古康宁爆破有限责任公司，内蒙古鄂尔多斯 017010

基金项目: 国家自然科学基金（52274083）；云南省重大科技专项（202202AG050014）；云南省基础研究计划面上项目（202201AT070178）；浙江省自然资源科技项目（2024ZJDZ026）

详细信息

作者简介:
左　庭（1993－　），男，博士研究生，ztkust@163.com

通讯作者:
李祥龙（1981－　），男，博士，教授，lxl00014002@163.com

中图分类号: O346.1
计量
- 文章访问数: 91
- HTML全文浏览量: 16
- PDF下载量: 35
- 被引次数: 0
出版历程
- 收稿日期: 2024-06-30
- 修回日期: 2024-10-26
- 网络出版日期: 2024-11-13

Numerical modeling of the energy dissipation and fragmentation of copper-bearing rock under impact load

ZUO Ting^{1, 2
,},
LI Xianglong^{1, 2
, ,},
WANG Jianguo^{1, 2},
HU Qiwen^{1, 2},
TAO Zihao^{1, 2},
HU Tao^{1, 2},
ZHANG Binbin³,
SONG Jiawang⁴

1.
Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming 650093, Yunnan, China
2.
Advanced Blasting Technology Engineering Research Center of Yunnan Provincial Department of Education, Kunming 650093, Yunnan, China
3.
Nuclear Industry Jingxiang Construction Group Co., Ltd., Huzhou 313000, Zhejiang, China
4.
Inner Mongolia Knergy Blasting Co., Ltd., Ordos 017010, Inner Mongolia, China

摘要

摘要: 为了研究冲击荷载作用下含铜矿岩的破碎块度与能量耗散关系，借助分离式霍普金森压杆试验装置，分析不同冲击荷载下含铜凝灰岩的力学特性及能量传递规律，结合分形理论构建耗散能与矿岩破碎块度之间关系。同时基于有限离散元方法（finite discrete element method，FDEM）模拟矿岩的裂纹扩展行为。结果表明：随着入射能的增加，透射能、耗散能、反射能三者的能量分布规律基本保持一致，即透射能、耗散能、反射能依次降低；根据耗散能的不同，碎石块度分布也呈现出明显的差异性。当耗散能由19.52 J提升至105.72 J时，矿岩的平均块度从27.98 mm降低至16.94 mm，分形维数提升了26.43%，表明耗散能越高，矿岩的宏观破碎程度越剧烈，破碎块度的数目越多，碎块粒径越小，均匀性越好；随着冲击荷载的增大，裂纹起裂时间缩短，拉伸裂纹数量占总裂纹数量的比重提高。FDEM数值计算方法的应用为深入解析岩石断裂破坏特性提供了新的思路。
- 分离式霍普金森压杆 /
- 含铜矿岩 /
- 破碎块度 /
- 分形维数 /
- 能量耗散 /
- 有限离散元
Abstract: To understand the relationship between fragmentation and energy dissipation in copper-bearing ore rock subjected to impact loading, a split Hopkinson pressure bar (SHPB) testing apparatus was employed to study the mechanical properties and energy transfer mechanisms of copper-bearing tuff under varying impact loads. Additionally, fractal theory was used to establish the correlation between dissipated energy and rock fragmentation. Utilizing the finite discrete element method (FDEM), numerical simulations of crack propagation within the rock were conducted. The results indicate that as the incident energy increases, the distribution patterns of the transmission energy, absorbed energy and reflection energy remain consistent, which are characterized by transmission energy, absorbed energy and reflection energy decreased successively. Furthermore, significant variations in fragment size distribution are observed with changes in dissipated energy. Specifically, as dissipated energy increases from 19.52 J to 105.72 J, the average fragment size decreases from 27.98 mm to 16.94 mm, while the fractal dimension increases by 26.43%. This suggests that higher dissipated energy results in more extensive macroscopic fragmentation, an increase in the number of fragments, smaller particle sizes and enhanced uniformity. As the impact load intensifies, the time to crack initiation decreases, and the proportion of tensile cracks relative to total cracks increases. The application of the FDEM offers new insights into the fracture and failure characteristics of rocks.
- split Hopkinson pressure bar /
- copper-bearing rock /
- fragmentation /
- fractal dimension /
- energy dissipation /
- finite discrete element method

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图 1 SHPB试验装置

Figure 1. SHPB test device

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图 2 含铜凝灰岩试件

Figure 2. Copper bearing rock specimen

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图 3 动态应力平衡

Figure 3. Dynamic stress balance

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图 4 冲击气压与入射能曲线关系

Figure 4. Relationship between impact pressure and incident energy curve

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图 5 能量时程曲线

Figure 5. Energy-time history curves

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图 6 冲击荷载下含铜矿岩能量比率传递规律

Figure 6. Energy ratio transfer of copper bearing rock under impact load

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图 7 不同耗散能下含铜矿岩的破碎模式

Figure 7. Fracture patterns of copper bearing rocks under different dissipated energies

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图 8 不同耗散能与含铜矿岩破碎块度分布

Figure 8. Mass distribution against fragment size for different absorbed energy by copper bearing rocks

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图 9 不同耗散能与矿岩破碎块度的分布

Figure 9. Distribution of copper-bearing rock fragmentation for different dissipated energies

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图 10 不同耗散能条件下典型lg[M(r)/M_T]-lgr关系曲线

Figure 10. Typical lg [M (r)/M_T]-lgr curves under different dissipated energies

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图 11 耗散能与分形维数关系曲线

Figure 11. Relationship between fractal dimension and dissipated energy

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图 12 FDEM基本原理

Figure 12. Schematic diagram of FDEM

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图 13 凝灰岩试件数值计算模型

Figure 13. Numerical model of Tuff specimen

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图 14 不同冲击气压下含铜凝灰矿岩的裂纹演变图（蓝色代表拉伸裂纹，红色代表剪切裂纹）

Figure 14. Crack evolution diagram of copper-bearing Tuff specimens under different impact air pressures (Blue - Tensile Cracks, Red - Shear Cracks)

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图 15 冲击气压对裂纹的影响规律

Figure 15. Effects of impact air pressure on cracking

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表 1 含铜矿岩基本物理力学参数

Table 1. Basic physical and mechanical parameters of copper bearing rock specimen

编号	密度/(g·cm⁻³)	纵波波速/(m·s⁻¹)	弹性模量/GPa	泊松比	抗压强度/MPa
J-1	3.10	3 549	93.35	0.33	59.23

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表 2 含铜矿岩的冲击实验数据

Table 2. SHPB test data of copper-bearing rock samples

编号	冲击气压/ MPa	平均应变率/s⁻¹	峰值应力/ MPa	W_I/J	W_R/J	W_T/J	W_D/J
A-3	0.5	30.68	108.03	63.34	7.24	45.13	10.62
B-2	0.6	35.71	119.72	81.67	5.73	55.75	19.51
C-4	0.7	44.25	141.35	105.92	7.32	66.10	31.57
D-1	0.8	50.93	163.19	130.76	8.05	74.19	47.75
E-3	0.9	53.62	189.55	168.28	23.94	83.45	60.60
F-2	1.0	59.15	200.93	203.33	37.88	89.99	75.12
G-4	1.1	64.81	249.80	222.91	43.46	93.01	85.52
H-1	1.2	77.39	265.90	267.09	62.21	99.06	105.72

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表 3 含铜矿岩破碎块度筛分试验结果

Table 3. Test screening results of crushed copper-bearing rock fragments

编号	W/J	各个等级粒径质量(0.01g)										平均块度/ mm
编号	W/J	<0.3 mm	<0.5 mm	<1.0 mm	<2.0 mm	<4.0 mm	<9.5 mm	<16.0 mm	<19.0 mm	<26.5 mm	<37.5 mm	平均块度/ mm
B2-0.6	19.52	0.04	0.18	0.13	0.31	0.16	1.35	2.95	12.8	36.44	123.42	27.98
C4-0.7	31.58	0.09	0.13	0.25	0.55	0.64	3.03	4.50	18.16	91.39	51.51	23.29
D1-0.8	47.75	0.11	1.52	2.46	3.74	3.39	12.10	18.87	24.19	47.12	53.92	20.54
E3-0.9	60.61	0.07	0.12	0.32	0.79	0.78	9.06	25.52	33.49	55.18	20.42	19.62
F2-1	75.13	0.1	0.24	0.54	1.33	1.25	9.85	40.75	39.61	22.46	20.47	18.28
G4-1.1	85.53	0.15	0.37	0.75	1.55	1.38	16.84	44.16	30.27	69.63	0	16.92
H3-1.2	105.72	0.27	0.68	1.20	2.60	1.92	20.17	51.22	32.99	46.95	12.74	16.94

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表 4 FDEM参数^[40]

Table 4. FDEM parameters^[40]

三角形单元					节理单元
ρ/(kg·m⁻³)	E/GPa	p_n/GPa	p_t/GPa	μ	c/MPa	f_t/MPa	ϕ/(°)	G_I/(J·m⁻²)	G_II/(J·m⁻²)	p_f/GPa
3080	65.00	65.00	65.00	0.28	5.26	8.26	30	1100	2200	6500

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