基于颗粒流方法的端部放矿力链特性研究
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摘要
为加深对端部放矿矿岩颗粒流动机理的认识,采用颗粒离散方法,通过均匀分布的球形颗粒描述矿岩块构成,设计了具有矿岩散体细观性质的三维无底柱数值模型,进行了放出体流动特性细观分析。利用接触力学方法计算矿岩流动过程中颗粒间的接触力和力网分布特征,计算结果表明:①放矿过程中颗粒间接触力与平均接触力的比值f不受放矿的影响,肯峰值约等于1,在f>1时服从幂函数关系,f<1时呈负指数关系;②颗粒内长度L大于3个颗粒数的力链概率服从e指数关系,一次放矿中力链较长的概率略有降低,但在任意时刻,均随着力链长度的增加而迅速下降;③放矿的全过程中,f∈[1,2]时接触力随出矿次数的增加而线性下降,但f>2时接触力不受放矿影响。
In order to deepen the understanding on the mechanism of ore-rock particle flow at the side ore-drawing,a three-dimensional numerical model without pillar was designed by using discrete element method and describing the composition of ore-rock block by uniformly distributed spherical particles,and the micro-analysis on the flow characteristics of orerock bulk was carried out. The contact force and force network distribution between particles in the process of ore-rock flow were calculated by the contact mechanics method. The results showed that: ① the ratio of contact force between particles and average contact force in the process of ore drawing is not affected by the ore drawing,and its peak value is about 1,which obeys power function when f > 1 and negative exponential function when f < 1;and ② the probability of force chain in which the inner length L is longer than 3 particles obeys the exponential relationship e. The exponential relationship shows that the probability of longer force chain in primary drawing decreases slightly,but it decreases rapidly with the increase of the length of force chain at any time. ③ in the whole process of ore drawing,the contact force decreases linearly with the increase of the times of ore drawing when f∈[1,2],but the contact force is not affected by ore drawing when f> 2.
In order to deepen the understanding on the mechanism of ore-rock particle flow at the side ore-drawing,a three-dimensional numerical model without pillar was designed by using discrete element method and describing the composition of ore-rock block by uniformly distributed spherical particles,and the micro-analysis on the flow characteristics of orerock bulk was carried out. The contact force and force network distribution between particles in the process of ore-rock flow were calculated by the contact mechanics method. The results showed that: ① the ratio of contact force between particles and average contact force in the process of ore drawing is not affected by the ore drawing,and its peak value is about 1,which obeys power function when f > 1 and negative exponential function when f < 1;and ② the probability of force chain in which the inner length L is longer than 3 particles obeys the exponential relationship e. The exponential relationship shows that the probability of longer force chain in primary drawing decreases slightly,but it decreases rapidly with the increase of the length of force chain at any time. ③ in the whole process of ore drawing,the contact force decreases linearly with the increase of the times of ore drawing when f∈[1,2],but the contact force is not affected by ore drawing when f> 2.
引文
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[16]Majmudar T S,BehringerR P.Contact force measurements and stress-induced anisotropy in granular materials[J].Nature,2005,435(23):1079-1082
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[18]赵闯,邓雄,胡林.三维受压剪切颗粒体系的力链结构[J].山东大学学报:理学版,2014,49(5):20-23.Zhao Chuang,Deng Xiong,Hu Lin.Force chains of the compressed and sheared granular matter in 3D[J].Journal of Shandong University:Natural Science,2014,49(5):20-23.
[19]王光谦,孙其诚.颗粒物质及其多尺度结构统计规律[J].工程力学,2009,26(SⅡ):1-7.Wang Guangqian,Sun Qicheng.Granular matter and the scaling laws[J].Engineering Mechanics,2009,26(SⅡ):1-7.
[2]任凤玉.随机介质放矿理论及其应用[M].北京:冶金工业出版社,1994.Ren Fengyu.Theory and Application of Ore Drawing in Random Medium[M].Beijing:Metallurgical Industry Press,1994.
[3]Castro R,Trueman R,Halim A.A study of isolated draw zones in block caving mines by means of a large 3D physical model[J].International Journal of Rock Mechanics and Mining Sciences,2007,44(6):860-870.
[4]陶干强,杨仕教,任凤玉.崩落矿岩散粒体流动性能实验研究[J].岩土力学,2009,30(10):2950-2054.Tao Ganqiang,Yang Shijiao,Ren Fengyu.Experimental research on granular flow characters of caved ore and rock[J].Rock Soil Mech,2009,30(10):2950-2054.
[5]陶干强,任青云,马娇阳.基于运动学模型的多漏口放矿规律[J].煤炭学报,2012,37(3):407-410.Tao Ganqiang,Ren Qingyun,Ma Jiaoyang.Ore drawing rules produced by poly-drawpoints based on kinematic mode[lJ].Journal of China Coal Society,2012,37(3):407-410.
[6]孙其诚,王光谦.颗粒物质力学导论[M].北京:科学出版社,2009.Sun Qicheng,Wang Guangqian.Introduction to Particle Mechanics[M].Beijing:Science Press,2009.
[7]Melo F,Vivanco F,Fuentes C,et al.On draw body shapes:from Bergmark-Roos to kinematic models[J].International Journal of Rock Mechanics&Mining Sciences,2007,44(1):77-86.
[8]安龙,徐帅,李元辉,等.基于多方法联合的崩落法崩矿步距优化[J].岩石力学与工程学报,2013,32(4):754-759.An Long,Xu Shuai,Li Yuanhui,et al.Optimization of rate of advance during ore breaking of caving method based on multi-method joint application[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(4):754-759.
[9]孙浩,金爱兵,高永涛,等.崩落法采矿中放出体流动特性的影响因素[J].工程科学学报,2015,37(9):1111-1117.Sun Hao,Jin Aibing,Gao Yongtao,et al.Influencing factors on the flow characteristics of an isolated extraction zone in caving mining[J].Chinese Journal of Engineering,2015,37(9):1111-1117.
[10]Sun Qicheng,Wang Guangqian,Hu Kaiheng.Some open problems in granular matter mechanics[J].Progress in Natural Science,2009,19(5):523-529.
[11]Gates M E,Wittmer J P,Bouchaud J P,et al.Jamming and stress propagation in particulate matter[J].Physica Section A:Statistical Mechanics and Its Applications,1999,263(1-4):354-361.
[12]Cundall P A,Strack O D L.A discrete numerical model for granular assemblies[J].Geotechnique,1979,29(1):47-65.
[13]Tordesillas Antoinette,Shi Jingyu,Tshaikiwsky Timothy.Stressdilatancy and force chain evolution[J].International Journal for Numerical and Analytical Methods in Geomechanics,2011,35(2):264-292.
[14]Sun Qicheng,Jin Feng,Wang Guangqian,et al.Force chains in a uniaxially compressed static granularmatter in 2D[J].Acta Physica Sinica,2010,59(1):30-37.
[15]Micha-Klaus Muller,Stefan Luding,Thorsten Poschel.Force statistics and correlations in dense granular packings[J].Chemical Physics,2010,375(2-3):600-605.
[16]Majmudar T S,BehringerR P.Contact force measurements and stress-induced anisotropy in granular materials[J].Nature,2005,435(23):1079-1082
[17]Farhang Radjai,Michel Jean,Jean-Jacques Moreau,et al.Force distributions in dense two-dimensional granular systems[J].Physical Review Let,1996,77(2):274-277.
[18]赵闯,邓雄,胡林.三维受压剪切颗粒体系的力链结构[J].山东大学学报:理学版,2014,49(5):20-23.Zhao Chuang,Deng Xiong,Hu Lin.Force chains of the compressed and sheared granular matter in 3D[J].Journal of Shandong University:Natural Science,2014,49(5):20-23.
[19]王光谦,孙其诚.颗粒物质及其多尺度结构统计规律[J].工程力学,2009,26(SⅡ):1-7.Wang Guangqian,Sun Qicheng.Granular matter and the scaling laws[J].Engineering Mechanics,2009,26(SⅡ):1-7.