Fig. 1. Granular computing iteration diagram: (a) Relationship between force and displacement; (b) theoretical computing.
Fig. 2. The forces by particles interacting.
Fig. 3. Diagram of normal force of granular: (a) Normal overlap; (b) position relations.
Fig. 4. Diagram of sliding accumulation model of loose accumulation body: (a) Three-dimensional numerical model; (b) side of view; (c) vertical view.
Fig. 5. Diagram large sample of single particle: (a) – Z of view; (b) +Y of view.
Fig. 6. Comparison of cumulative volume between experiment results
[30] and DEM simulation results of granular after sliding.
Fig. 7. Loose materials the whole process of sliding accumulation(+X view): (a) t = 400 ms; (b) t = 600 ms; (c) t = 860 ms; (d) t = 1 000 ms; (e) t = 1 200 ms; (f) t = 2 000 ms; (g) accumulation process changes shape.
Fig. 8. The final diagram of plane accumulation form.
Fig. 9. Influence of stone content on the accumulation form: (a) Stroke; (b) accumulation width; (c) maximum thickness; (d) accumulation area.
Fig. 10. Static accumulation angle boundary contour acquire.
Fig. 11. Schematic diagram of volume calculation of accumulation area.
Fig. 12. Influence of different stone contents on the accumulation volume at a slope of 65°.
Fig. 13. Influence of slope on the accumulation form: (a) Stroke; (b) accumulation width; (c) maximum thickness; (d) accumulation area.
Fig. 14. Plane accumulation morphology under different slope: (a) Stone content 0%; (b) stone content 30%; (c) stone content 50%; (d) stone content 70%.
Fig. 15. The results of the sliding accumulation simulation of stone content 50% loose granular with different slopes: (a) 30°; (b) 45°; (c) 65°.
Fig. 16. Influence of different slope of 50% stone content on the accumulation volume.
Fig. 17. The volume comparison of granular with different slopes with 50% stone content: (a) 30°; (b) 45°; (c) 65°.
Fig. 18. Influence of different stone contents on cumulative mass at slope of 65°.
Fig. 19. Influence of different slope on cumulative mass at stone content of 50%.
Fig. 20. The cumulative mass comparison of granular with different slopes with 50% stone content: (a) 30°; (b) 45°; (c) 65°.
Fig. 21. Granular average kinetic energy distribution characteristics: (a)Translational kinetic energy; (b) rotational kinetic energy.
Fig. 22. Time-history curve of average normal contact force between granulars: (a) x direction; (b) y direction; (c) z direction.
Fig. 23. Time-history curve of average tangential contact force between granulars: (a) x direction; (b) y direction; (c) z direction.
Fig. 24. Time-history curve of average contact force overlap between granulars: (a) Normal; (b) tangential.
Fig. 25. Probability density functions (PDF) of average normal contact force between granulars: (a) x direction; (b) y direction; (c) z direction.
参数 | 符号 | 单位 | 数值 | | 参数 | 符号 | 单位 | 数值 | 细颗粒基础球粒径 | d | mm | 4.00 | | 静摩擦系数 | μps | — | 0.44 | 粗颗粒基础球粒径 | d | mm | 14.00 | | 滚动摩擦系数 | μpr | — | 0.05 | 颗粒密度 | ρ | kg/m3 | 2100.00 | | 堆积体质量 | M | kg | 30.00 | 剪切模量 | E | MPa | 1000.00 | | 时间步长 | dt | s | 6.26616 × 10–5 | 泊松比 | v | — | 0.26 | | 滑槽尺寸 | L × W × H | mm | 1800 × 350 × 300 | 恢复系数 | e | — | 0.40 | | 底板尺寸 | L × W × H | mm | 3000 × 2000 × 10 | 摩擦系数 | μpp | — | 0.42 | | 料箱尺寸 | l × w × h | mm | 400 × 350 × 200 |
|
Table 1. Main computational parameters of discrete element simulation for loose granular accumulation.
松散颗粒堆积离散元模拟的主要计算参数
计算条件 | +X方向γ /(°)
| -X方向γ /(°)
| 均值γ /(°)
| 30° 0% | 13.58 | 13.46 | 13.52 | 30° 30% | 12.94 | 13.13 | 13.40 | 30° 50% | 12.48 | 13.32 | 12.90 | 30° 70% | 12.03 | 11.27 | 11.65 | 45° 0% | 8.25 | 8.21 | 8.23 | 45° 30% | 6.85 | 7.31 | 7.08 | 45° 50% | 7.28 | 6.92 | 7.10 | 45° 70% | 7.78 | 7.24 | 7.51 | 65° 0% | 4.17 | 4.28 | 2.23 | 65° 30% | 4.25 | 4.59 | 2.42 | 65° 50% | 4.26 | 4.89 | 2.58 | 65° 70% | 4.96 | 4.74 | 2.85 |
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Table 2. Measured value of static accumulation angle under different computing conditions.
不同计算条件下静堆积角测量值
参量 | 细颗粒 | 粗颗粒 | 细颗粒与粗颗粒 | 平均平动动能Et/10–4 J
| 2.41 | 169.28 | — | 平均转动动能Er/10–7 J
| 4.66 | 26.03 | — | 平均法向力Fn/10–6 N
| 19.04 | 155.37 | 31.77 | 平均切向力Ft/10–3 N
| 6.84 | 55.37 | 11.36 | 平均法向重叠量/ 10–2 mm
| 4.01 | 10.13 | 4.77 | 平均切向重叠量/ 10–2 mm
| 1.05 | 2.87 | 1.27 |
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Table 3. Average kinetic energy and contact force of granular in the process of sliding accumulation.
滑动堆积过程中颗粒的平均动能和接触力均值
模拟变量 | 模拟结果 | 冲程 | 堆积宽度 | 最大厚度 | 堆积面积 | 累积质量 | 静堆积角 | 注: 1. 表中所考虑的均是模拟变量数值增大对模拟结果的影响; 其中, 含石量σ (%)的取值分别为0, 30, 50, 70; 坡度θ (°)的取值分别为30, 45, 65. 2. “↗”表示模拟结果持续增大, “↘”表示模拟结果持续减小; “↗ ↘”表示模拟结果先增大后持续减小, “↘ ↗”表示模拟结果先减小后持续增大, “↗ ↗”表示模拟结果增大明显, “↘ ↘”表示模拟结果减小明显, “↘(较小)”表示模拟结果小幅度减小, “↗(较小)”表示模拟结果小幅度增大.
| 含石量 | ↗↘ | ↗↘ | ↘↗ | ↗↘ | ↘(较小) | ↘(较小)或↗(较小) | 坡度 | ↗↗ | ↗ | ↘ | ↗↗ | ↗↗ | ↘↘ |
|
Table 4. Summary table of simulation results.
模拟结果汇总表