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Loose materials has loose structure and is the main source of geological disasters such as collapses and landslides. Its hazard range is greatly affected by factors such as stone content and slope. Traditional studies on the sliding and accumulation characteristics of loose materials were mostly macro or qualitative analysis. There is little research on the micro internal motion mechanism. In the present study, discrete element method was used to quantitatively analyze the influence of stone content and slope variation on the characteristic values of loose particles such as stroke, accumulation width, maximum thickness, accumulation area, accumulation contour shape, accumulation volume, static accumulation angle and the cumulative mass. In the meanwhile, the movement and accumulation characteristics of the loose materials during the catastrophe process were explored from the aspect of energy and contact force of the particles, so as to reveal the interaction mechanism between the particles. The results showed that: When the stone content increased in the range of 0 to 70%, the stroke, accumulation width and accumulation area increased firstly and then decreased, and in the end the cumulative mass decreased. As the slope increased from 30° to 65°, the stroke, accumulation width, accumulation area and accumulation mass increased; the maximum thickness decreased approximately linearly, while the static accumulation angle had a decrease similar to quadratic function. In addition, there was a critical distance Lc for the volume share of coarse and fine particles in the accumulation area. When the distance from the toe line was L < Lc, the fine particles were larger than the volume of the coarse particles; when L > Lc, the fine particles were smaller than the volume occupied by coarse particles.
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Keywords:
- loose materials /
- accumulation characteristics /
- non-spherical particle /
- discrete element method
[1] 赵永志, 江茂强, 徐平, 郑津洋 2009 物理学报 58 1819
Google Scholar
Zhao Y Z, Jiang M Q, Xu P, Zheng J Y 2009 Acta Phys. Sin. 58 1819
Google Scholar
[2] Hsü K J 1975 Geol. Soc. Am. Bull. 86 129
Google Scholar
[3] 贺可强, 周敦云, 王思敬 2004 岩石力学与工程学报 23 2665
Google Scholar
He K Q, Zhou D Y, Wang S J 2004 Chin. J. Rock Mech. Eng. 23 2665
Google Scholar
[4] Lin G W, Chen H, Hovius N, Horng M J, Dadson S, Meunier P, Lines M 2008 Earth Surf. Process. Landf. 33 1354
Google Scholar
[5] 曹叔尤, 刘兴年 2016 四川大学学报(工程科学版) 48 1
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Cao S Y, Liu X N 2016 J. Sichuan Univ. (Engineering Science Edition) 48 1
Google Scholar
[6] 雷明, 许泽星, 刘兴年, 王协康 2018 工程科学与技术 50 240
Google Scholar
Lei M, Xu Z X, Liu X N, Wang X K 2018 Adv. Eng. Sci. 50 240
Google Scholar
[7] 雷先顺, 谢沃, 卢坤林, 朱大勇, 陈菊香 2016 岩土工程学报 38 226
Google Scholar
Lei X S, Xie W, Lu K L, Zhu D Y, Chen J X 2016 Chin. J. Geotech. Eng. 38 226
Google Scholar
[8] 罗伟韬 2014 硕士学位论文 (北京: 清华大学)
Luo W T 2014 M. S. Thesis (Beijing: Tsinghua University) (in Chinese)
[9] Davies T R, Mcsaveney M J 1999 Can. Geotech. J. 36 313
Google Scholar
[10] Joachim S, Carlo F 2003 Eng. Geol. 67 281
Google Scholar
[11] Scheiddeger A E 1973 Rock Mech. 5 231
Google Scholar
[12] Ritchie A M 1963 Highw. Res. Rec. 17 13
[13] Mancarella D, Hungr O 2010 Can. Geotech. J. 47 827
Google Scholar
[14] Mindlin R D 1949 J. Appl. Mech. 16 259
Google Scholar
[15] Tsuji Y, Tanaka T, Ishida T 1992 Powder Technol. 71 239
Google Scholar
[16] Potyondy D, Cundall P A 2004 Int. J. Rock Mech. Min. Sci. 41 1329
Google Scholar
[17] 韩燕龙, 贾富国, 唐玉荣, 刘扬, 张强 2014 物理学报 63 174501
Google Scholar
Han Y L, Jia F G, Tang Y R, Liu Y, Zhang Q 2014 Acta Phys. Sin. 63 174501
Google Scholar
[18] Nakashima H, Shioji Y, Kobayashi T, Aoki S, Shimizu H, Miyasaka J, Ohdoi K 2011 J. Terramechanics 48 17
Google Scholar
[19] Zhou Y C, Xu B H, Yu A B, Zulli P 2002 Powder Technol. 125 45
Google Scholar
[20] Okura Y, Kitahara H, Sammori T 2000 Eng. Geol. 56 347
Google Scholar
[21] Okura Y, Kitahara H, Sammori T, Kawanami A 2000 Eng. Geol. 58 109
Google Scholar
[22] Davies T, Mcsaveney M, Hodgson K A 1999 Can. Geotech. J. 36 1096
[23] Davies T 1982 Rock Mech. 15 9
Google Scholar
[24] Cundall P A & Strack O D L 1979 Geotechnique 29 47
Google Scholar
[25] 王国强, 郝万军, 王继新 2010 离散单元法及其在EDEM上的实践 (西安: 西北工业大学出版社) 第15—18页
Wang G Q, Hao W J, Wang J X 2010 Discrete Element Method and its Practice on EDEM (Vol. 1) (Xian: Northwestern Polytechnical University Press) pp15–18 (in Chinese)
[26] Jiang Y J, Zhao Y, Towhata I, Liu D X 2015 Powder Technol. 270 53
Google Scholar
[27] Jiang Y J, Towhata I 2013 Rock Mech. Rock Eng. 46 713
Google Scholar
[28] 舒志乐, 刘新荣, 刘保县, 李月 2010 中南大学学报(自然科学版) 41 1096
Shu Z L, Liu X R, Liu B X, Li Y 2010 J. Cent. South Univ.(Science and Technology) 41 1096
[29] 杨海龙 2018 硕士学位论文 (绵阳: 西南科技大学)
Yang H L 2018 M. S. Thesis (Mianyang: Southwest University of Science and Technology) (in Chinese)
[30] Zhou J W, Yang X G, Hou T X 2017 Environ. Earth Sci. 76 452
Google Scholar
[31] 赵啦啦, 刘初升, 闫俊霞, 徐志鹏 2010 物理学报 59 1870
Google Scholar
Zhao L L, Liu C S, Yan J X, Xu Z P 2010 Acta Phys. Sin. 59 1870
Google Scholar
[32] Langston P A, Awamleh M A, Fraige F Y, Asmar B N 2004 Chem. Eng. Sci. 59 425
Google Scholar
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图 1 颗粒计算迭代示意图 (a) 力与位移关系; (b) 理论计算
Figure 1. Granular computing iteration diagram: (a) Relationship between force and displacement; (b) theoretical computing.
图 2 颗粒相互作用时的受力
Figure 2. The forces by particles interacting.
图 3 颗粒法向力示意图 (a) 法向重叠量; (b) 位置关系
Figure 3. Diagram of normal force of granular: (a) Normal overlap; (b) position relations.
图 4 松散体滑动堆积模型示意图 (a) 三维数值模型; (b) 侧视图; (c) 俯视图
Figure 4. Diagram of sliding accumulation model of loose accumulation body: (a) Three-dimensional numerical model; (b) side of view; (c) vertical view.
图 5 单个颗粒大样图 (a) –Z视角; (b) +Y视角
Figure 5. Diagram large sample of single particle: (a) –Z of view; (b) +Y of view.
图 7 松散体滑动堆积全过程(+X视角) (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) 堆积过程形状变化
Figure 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.
图 8 最终平面堆积形态示意图
Figure 8. The final diagram of plane accumulation form.
图 9 含石量对堆积形态的影响 (a) 冲程; (b) 堆积宽度; (c) 最大厚度; (d) 堆积面积
Figure 9. Influence of stone content on the accumulation form: (a) Stroke; (b) accumulation width; (c) maximum thickness; (d) accumulation area.
图 10 静堆积角边界轮廓提取
Figure 10. Static accumulation angle boundary contour acquire.
图 11 堆积区体积计算平面示意图
Figure 11. Schematic diagram of volume calculation of accumulation area.
图 12 坡度65°时不同含石量对堆积体积的影响
Figure 12. Influence of different stone contents on the accumulation volume at a slope of 65°.
图 13 坡度对堆积形态的影响 (a) 冲程; (b) 堆积宽度; (c) 最大厚度; (d) 堆积面积
Figure 13. Influence of slope on the accumulation form: (a) Stroke; (b) accumulation width; (c) maximum thickness; (d) accumulation area.
图 14 不同坡度下的堆积轮廓平面形状 (a) 含石量0%; (b) 含石量30%; (c) 含石量50%; (d) 含石量70%
Figure 14. Plane accumulation morphology under different slope: (a) Stone content 0%; (b) stone content 30%; (c) stone content 50%; (d) stone content 70%.
图 15 含石量50%时不同坡度松散颗粒滑动堆积模拟结果 (a) 30°; (b) 45°; (c) 65°
Figure 15. The results of the sliding accumulation simulation of stone content 50% loose granular with different slopes: (a) 30°; (b) 45°; (c) 65°.
图 16 含石量50%时不同坡度对堆积体积的影响
Figure 16. Influence of different slope of 50% stone content on the accumulation volume.
图 17 含石量50%时不同坡度颗粒体积对比 (a) 30°; (b) 45°; (c) 65°
Figure 17. The volume comparison of granular with different slopes with 50% stone content: (a) 30°; (b) 45°; (c) 65°.
图 18 坡度65°时不同含石量对累积质量的影响
Figure 18. Influence of different stone contents on cumulative mass at slope of 65°.
图 19 含石量50%时不同坡度对累积质量的影响
Figure 19. Influence of different slope on cumulative mass at stone content of 50%.
图 20 含石量50%时各坡度颗粒累积质量对比 (a) 30°; (b) 45°; (c) 65°
Figure 20. The cumulative mass comparison of granular with different slopes with 50% stone content: (a) 30°; (b) 45°; (c) 65°.
图 21 颗粒平均动能分布特性 (a) 平动动能; (b) 转动动能
Figure 21. Granular average kinetic energy distribution characteristics: (a)Translational kinetic energy; (b) rotational kinetic energy.
图 25 颗粒间平均法向接触力概率密度函数(PDF)分布 (a) x方向; (b) y方向; (c) z方向
Figure 25. Probability density functions (PDF) of average normal contact force between granulars: (a) x direction; (b) y direction; (c) z direction.
图 22 颗粒间平均法向接触力时程曲线 (a) x方向; (b) y方向; (c) z方向
Figure 22. Time-history curve of average normal contact force between granulars: (a) x direction; (b) y direction; (c) z direction.
图 23 颗粒间平均切向接触力时程曲线 (a) x方向; (b) y方向; (c) z方向
Figure 23. Time-history curve of average tangential contact force between granulars: (a) x direction; (b) y direction; (c) z direction.
图 24 颗粒间平均接触力重叠量时程曲线 (a) 法向; (b) 切向
Figure 24. Time-history curve of average contact force overlap between granulars: (a) Normal; (b) tangential.
表 1 松散颗粒堆积离散元模拟的主要计算参数
Table 1. Main computational parameters of discrete element simulation for loose granular accumulation.
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 
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表 2 不同计算条件下静堆积角测量值
Table 2. Measured value of static accumulation angle under different computing conditions.
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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表 3 滑动堆积过程中颗粒的平均动能和接触力均值
Table 3. Average kinetic energy and contact force of granular in the process of sliding accumulation.
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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表 4 模拟结果汇总表
Table 4. Summary table of simulation results.
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 含石量 ↗↘ ↗↘ ↘↗ ↗↘ ↘(较小) ↘(较小)或↗(较小) 坡度 ↗↗ ↗ ↘ ↗↗ ↗↗ ↘↘ 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.
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[1] 赵永志, 江茂强, 徐平, 郑津洋 2009 物理学报 58 1819
Google Scholar
Zhao Y Z, Jiang M Q, Xu P, Zheng J Y 2009 Acta Phys. Sin. 58 1819
Google Scholar
[2] Hsü K J 1975 Geol. Soc. Am. Bull. 86 129
Google Scholar
[3] 贺可强, 周敦云, 王思敬 2004 岩石力学与工程学报 23 2665
Google Scholar
He K Q, Zhou D Y, Wang S J 2004 Chin. J. Rock Mech. Eng. 23 2665
Google Scholar
[4] Lin G W, Chen H, Hovius N, Horng M J, Dadson S, Meunier P, Lines M 2008 Earth Surf. Process. Landf. 33 1354
Google Scholar
[5] 曹叔尤, 刘兴年 2016 四川大学学报(工程科学版) 48 1
Google Scholar
Cao S Y, Liu X N 2016 J. Sichuan Univ. (Engineering Science Edition) 48 1
Google Scholar
[6] 雷明, 许泽星, 刘兴年, 王协康 2018 工程科学与技术 50 240
Google Scholar
Lei M, Xu Z X, Liu X N, Wang X K 2018 Adv. Eng. Sci. 50 240
Google Scholar
[7] 雷先顺, 谢沃, 卢坤林, 朱大勇, 陈菊香 2016 岩土工程学报 38 226
Google Scholar
Lei X S, Xie W, Lu K L, Zhu D Y, Chen J X 2016 Chin. J. Geotech. Eng. 38 226
Google Scholar
[8] 罗伟韬 2014 硕士学位论文 (北京: 清华大学)
Luo W T 2014 M. S. Thesis (Beijing: Tsinghua University) (in Chinese)
[9] Davies T R, Mcsaveney M J 1999 Can. Geotech. J. 36 313
Google Scholar
[10] Joachim S, Carlo F 2003 Eng. Geol. 67 281
Google Scholar
[11] Scheiddeger A E 1973 Rock Mech. 5 231
Google Scholar
[12] Ritchie A M 1963 Highw. Res. Rec. 17 13
[13] Mancarella D, Hungr O 2010 Can. Geotech. J. 47 827
Google Scholar
[14] Mindlin R D 1949 J. Appl. Mech. 16 259
Google Scholar
[15] Tsuji Y, Tanaka T, Ishida T 1992 Powder Technol. 71 239
Google Scholar
[16] Potyondy D, Cundall P A 2004 Int. J. Rock Mech. Min. Sci. 41 1329
Google Scholar
[17] 韩燕龙, 贾富国, 唐玉荣, 刘扬, 张强 2014 物理学报 63 174501
Google Scholar
Han Y L, Jia F G, Tang Y R, Liu Y, Zhang Q 2014 Acta Phys. Sin. 63 174501
Google Scholar
[18] Nakashima H, Shioji Y, Kobayashi T, Aoki S, Shimizu H, Miyasaka J, Ohdoi K 2011 J. Terramechanics 48 17
Google Scholar
[19] Zhou Y C, Xu B H, Yu A B, Zulli P 2002 Powder Technol. 125 45
Google Scholar
[20] Okura Y, Kitahara H, Sammori T 2000 Eng. Geol. 56 347
Google Scholar
[21] Okura Y, Kitahara H, Sammori T, Kawanami A 2000 Eng. Geol. 58 109
Google Scholar
[22] Davies T, Mcsaveney M, Hodgson K A 1999 Can. Geotech. J. 36 1096
[23] Davies T 1982 Rock Mech. 15 9
Google Scholar
[24] Cundall P A & Strack O D L 1979 Geotechnique 29 47
Google Scholar
[25] 王国强, 郝万军, 王继新 2010 离散单元法及其在EDEM上的实践 (西安: 西北工业大学出版社) 第15—18页
Wang G Q, Hao W J, Wang J X 2010 Discrete Element Method and its Practice on EDEM (Vol. 1) (Xian: Northwestern Polytechnical University Press) pp15–18 (in Chinese)
[26] Jiang Y J, Zhao Y, Towhata I, Liu D X 2015 Powder Technol. 270 53
Google Scholar
[27] Jiang Y J, Towhata I 2013 Rock Mech. Rock Eng. 46 713
Google Scholar
[28] 舒志乐, 刘新荣, 刘保县, 李月 2010 中南大学学报(自然科学版) 41 1096
Shu Z L, Liu X R, Liu B X, Li Y 2010 J. Cent. South Univ.(Science and Technology) 41 1096
[29] 杨海龙 2018 硕士学位论文 (绵阳: 西南科技大学)
Yang H L 2018 M. S. Thesis (Mianyang: Southwest University of Science and Technology) (in Chinese)
[30] Zhou J W, Yang X G, Hou T X 2017 Environ. Earth Sci. 76 452
Google Scholar
[31] 赵啦啦, 刘初升, 闫俊霞, 徐志鹏 2010 物理学报 59 1870
Google Scholar
Zhao L L, Liu C S, Yan J X, Xu Z P 2010 Acta Phys. Sin. 59 1870
Google Scholar
[32] Langston P A, Awamleh M A, Fraige F Y, Asmar B N 2004 Chem. Eng. Sci. 59 425
Google Scholar
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