.1128 工程科学学报，第42卷，第9期 (5)多漏斗放矿过程中力链准直系数随着放矿 Eng2016,38(7):893 次数的增加呈指数形式增长并逐渐保持稳定 (陈庆发，陈青林，仲建字，等.柔性隔离层下单漏斗散体矿岩流 动规律.工程科学学报，2016,38(7)：893) 参考文献 [11]Chen Q F,Chen Q L,Zhong J Y,et al.Evolution law of interface [1]Littlewood D.Corporate social responsibility,mining and morphology of flexible isolation layer under ore drawing from sustainable development in Namibia:critical reflections through a single funnel.ChinJ Nonferrous Met,2016,26(6):1332 relational lens.Dev South Afr,2015,32(2):240 (陈庆发，陈青林，仲建宇，等.单漏斗放矿柔性隔离层界面形态 [2]Soni A K,Wolkersdorfer C.Mine water:policy perspective for 演化规律.中国有色金属学报，2016,26(6)：1332) [12]Chen Q F,Zhao F Y,Chen Q L,et al.Mechanical properties improving water management in the mining environment with analysis for a flexible isolation layer material in multiple funnels respect to developing economies.Int J Min Reclam Environ,2016. synchronous ore drawing based on an indoor model experiment. 30(2):115 Eng Mech,2018,35(11)：片240 [3]Chen Q F,Su J H.Synergetic mining and itstechnology system.J (陈庆发，赵富裕，陈青林，等.基于室内模型试验的多漏斗同步 Cent South Uniy Sci Technol,2013,44(2):732 放矿柔性隔离层材料受力特性分析.工程力学，2018,35(11)： (陈庆发，苏家红，协同开采及其技术体系.中南大学学报：自然 240) 科学版，2013,44(2)：732) [13]Tordesillas A,Shi J Y,Muhlhaus H B.Noncoaxiality and force [4]Chen Q F,Wu Z X.A Large Number ofOre Drawing Synchronous chain evolution.IntJ Eng Sci,2009,47(11-12):1386 Filling No-top-pillar Shrinkage Stoping Method:China Patent, [14]Hunt G W,Tordesillas A,Green S C,et al.Force-chain buckling 201010181971.2.2010-10-20 in granular media:a structural mechanics perspective.Philos Trans (陈庆发，吴仲雄.大量放矿同步充填无顶柱留矿采矿方法：中 R Soc A:Math Phrys Eng Sci,2010,368(1910):249 国专利，201010181971.2.2010-10-20) [15]Socolar J E S,Schaeffer D G,Claudin P.Directed force chain [5]Chen Q F,Qin S K,Chen QL.Numerical simulation of ore networks and stress response in static granular materials.Eur Phys particle flow behaviour through a single drawpoint under the JE,2002,7(4:353 influence of a flexible barrier.Geofluids,2019:6127174 [16]Estep J,Dufek J.Substrate effects from force chain dynamics in [6]Chen Q F,Qin S K,Chen Q L.Stress analysis of ore particle flow dense granular flows.J Geophys Res Earth Surf 2012,117(F1): behaviour under the influence of a flexible barrier.Arab/Geosci, 1028 2019,12(15):472 [17]Chen F X,Zhuang Q,Wang R L,et al.Damage point prediction of [7]Chen Q F,Zhao F Y,Chen Q L,et al.Orthogonal simulation a force chain based on the digital image correlation method.Appl experiment for flow characteristics of ore in ore drawing and 0p4,2017,56(3上636 influencing factors in a single funnel under a flexible isolation [18]Hou S Q,Wang W,Wang Z Y,et al.Force chain characteristics ayer.J0M,2017,69(12:2485 and effects of a dense granular flow system in a third body [8] Chen Q F,Chen QL,Wang Y D,et al.Study of the movement law interface during the shear dilatancy process.J Appl Mech Tech and tensile force character of flexible isolation layer interface in Ph3,2018,59(1):153 multiple funnels.J Basic Sci Eng,2018,26(5):1101 [19]Tordesillas A.Force chain buckling,unjamming transitions and (陈庆发，陈青林，王玉丁，等.多漏斗放矿柔性隔离层界面移动 shear banding in dense granular assemblies.Philos Mag,2007, 规律及其拉力特性.应用基础与工程科学学报，2018,26(5) 87(32):4987 1101) [20]Sun QC,Jin F,Liu J G,et al.Understanding force chains in dense [9]Chen Q F,Chen Q L,Zhong Y,et al.Orthogonal simulation test granular materials.Int Mod Phrys B,2010,24(29):5743 for flowing characteristics of ore-rock and influence factor in ore [21]Tordesillas A,Steer C A H,Walker D M.Force chain and contact drawing from multiple funnels under flexible isolation layer.Sci cycle evolution in a dense granular material under shallow Sin Tech,.2017,47(9:923 penetration.Nonlin Processes Geophys,2014,21(2):505 (陈庆发，陈青林，钟毓，等.柔性隔离层下多漏斗矿岩流动特性 [22]Zhang W.Zhou J,ZhangX J,et al.Quantitative investigation into 及影响因素正交模拟试验.中国科学：技术科学，2017,47(9)： the relation between force chains and stress transmission during 923) high-velocity compaction of powder.J Korean Phys Soc,2019, [10]Chen Q F,Chen QL.Zhong J Y.et al.Flow pattern of granular 74(7):660 ore rock in a single funnel under a flexible isolation layer.ChinJ [23]Zhang L R,Nguyen N G H,Lambert S,et al.The role of force（5）多漏斗放矿过程中力链准直系数随着放矿 次数的增加呈指数形式增长并逐渐保持稳定. 参    考    文    献 Littlewood  D.  Corporate  social  responsibility,  mining  and sustainable development in Namibia: critical reflections through a relational lens. Dev South Afr, 2015, 32（2）: 240 [1] Soni  A  K,  Wolkersdorfer  C.  Mine  water:  policy  perspective  for improving  water  management  in  the  mining  environment  with respect to developing economies. Int J Min Reclam Environ, 2016, 30（2）: 115 [2] Chen Q F, Su J H. Synergetic mining and itstechnology system. J Cent South Univ Sci Technol, 2013, 44（2）: 732 （陈庆发, 苏家红. 协同开采及其技术体系. 中南大学学报: 自然 科学版, 2013, 44（2）：732） [3] Chen Q F, Wu Z X. A Large Number of Ore Drawing Synchronous Filling No-top-pillar Shrinkage Stoping Method:  China  Patent, 201010181971.2. 2010-10-20 （陈庆发, 吴仲雄. 大量放矿同步充填无顶柱留矿采矿方法: 中 国专利, 201010181971.2. 2010-10-20） [4] Chen  Q  F,  Qin  S  K,  Chen  Q  L.  Numerical  simulation  of  ore particle  flow  behaviour  through  a  single  drawpoint  under  the influence of a flexible barrier. Geofluids, 2019: 6127174 [5] Chen Q F, Qin S K, Chen Q L. Stress analysis of ore particle flow behaviour under the influence of a flexible barrier. Arab J Geosci, 2019, 12（15）: 472 [6] Chen  Q  F,  Zhao  F  Y,  Chen  Q  L,  et  al.  Orthogonal  simulation experiment  for  flow  characteristics  of  ore  in  ore  drawing  and influencing  factors  in  a  single  funnel  under  a  flexible  isolation layer. JOM, 2017, 69（12）: 2485 [7] Chen Q F, Chen Q L, Wang Y D, et al. Study of the movement law and  tensile  force  character  of  flexible  isolation  layer  interface  in multiple funnels. J Basic Sci Eng, 2018, 26（5）: 1101 （陈庆发, 陈青林, 王玉丁, 等. 多漏斗放矿柔性隔离层界面移动 规律及其拉力特性. 应用基础与工程科学学报, 2018, 26（5）： 1101） [8] Chen Q F, Chen Q L, Zhong Y, et al. Orthogonal simulation test for flowing characteristics of ore-rock and influence factor in ore drawing  from  multiple  funnels  under  flexible  isolation  layer. Sci Sin Tech, 2017, 47（9）: 923 （陈庆发, 陈青林, 钟毓, 等. 柔性隔离层下多漏斗矿岩流动特性 及影响因素正交模拟试验. 中国科学: 技术科学, 2017, 47（9）： 923） [9] Chen Q F, Chen Q L, Zhong J Y, et al. Flow pattern of granular ore rock in a single funnel under a flexible isolation layer. Chin J [10] Eng, 2016, 38（7）: 893 （陈庆发, 陈青林, 仲建宇, 等. 柔性隔离层下单漏斗散体矿岩流 动规律. 工程科学学报, 2016, 38（7）：893） Chen Q F, Chen Q L, Zhong J Y, et al. Evolution law of interface morphology  of  flexible  isolation  layer  under  ore  drawing  from single funnel. Chin J Nonferrous Met, 2016, 26（6）: 1332 （陈庆发, 陈青林, 仲建宇, 等. 单漏斗放矿柔性隔离层界面形态 演化规律. 中国有色金属学报, 2016, 26（6）：1332） [11] Chen  Q  F,  Zhao  F  Y,  Chen  Q  L,  et  al.  Mechanical  properties analysis for a flexible isolation layer material in multiple funnels synchronous  ore  drawing  based  on  an  indoor  model  experiment. Eng Mech, 2018, 35（11）: 240 （陈庆发, 赵富裕, 陈青林, 等. 基于室内模型试验的多漏斗同步 放矿柔性隔离层材料受力特性分析. 工程力学, 2018, 35（11）： 240） [12] Tordesillas  A,  Shi  J  Y,  Muhlhaus  H  B.  Noncoaxiality  and  force chain evolution. Int J Eng Sci, 2009, 47（11-12）: 1386 [13] Hunt G W, Tordesillas A, Green S C, et al. Force-chain buckling in granular media: a structural mechanics perspective. Philos Trans R Soc A: Math Phys Eng Sci, 2010, 368（1910）: 249 [14] Socolar  J  E  S,  Schaeffer  D  G,  Claudin  P.  Directed  force  chain networks and stress response in static granular materials. Eur Phys J E, 2002, 7（4）: 353 [15] Estep  J,  Dufek  J.  Substrate  effects  from  force  chain  dynamics  in dense granular flows. J Geophys Res Earth Surf, 2012, 117（F1）: 1028 [16] Chen F X, Zhuang Q, Wang R L, et al. Damage point prediction of a force chain based on the digital image correlation method. Appl Opt, 2017, 56（3）: 636 [17] Hou S Q, Wang W, Wang Z Y, et al. Force chain characteristics and  effects  of  a  dense  granular  flow  system  in  a  third  body interface  during  the  shear  dilatancy  process. J Appl Mech Tech Phys, 2018, 59（1）: 153 [18] Tordesillas  A.  Force  chain  buckling,  unjamming  transitions  and shear  banding  in  dense  granular  assemblies. Philos Mag,  2007, 87（32）: 4987 [19] Sun Q C, Jin F, Liu J G, et al. Understanding force chains in dense granular materials. Int J Mod Phys B, 2010, 24（29）: 5743 [20] Tordesillas A, Steer C A H, Walker D M. Force chain and contact cycle  evolution  in  a  dense  granular  material  under  shallow penetration. Nonlin Processes Geophys, 2014, 21（2）: 505 [21] Zhang W, Zhou J, Zhang X J, et al. Quantitative investigation into the  relation  between  force  chains  and  stress  transmission  during high-velocity  compaction  of  powder. J Korean Phys Soc,  2019, 74（7）: 660 [22] [23] Zhang  L  R,  Nguyen  N  G  H,  Lambert  S,  et  al.  The  role  of  force · 1128 · 工程科学学报，第 42 卷，第 9 期