花岗岩球砾法向恢复系数试验研究
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摘要
法向恢复系数是岩崩块石运动分析的关键参数,其取值直接决定了块石的运动轨迹。为了严格测定花岗岩球砾碰撞的法向恢复系数,分析其影响因素,试验采用自行设计的碰撞试验装置和声频采样技术,精确测定花岗岩球砾碰撞的法向恢复系数,研究球砾大小、碰撞速度、含水状态和板的弹性特性4个因素对恢复系数的影响;并基于弹性接触理论推导出碰撞过程的最大接触应力P_(0,max)、碰撞起裂速度v_(ci)和碰撞损伤速度v_(cd),构造接触应力割线变化率k来描述碰撞过程的率相关,分析碰撞法向恢复系数的尺寸效应和速率效应,对碰撞过程耗能机制进行探讨。试验结果表明:花岗岩球砾法向恢复系数存在明显的尺寸效应,低速下更加显著;法向恢复系数的速率效应同样较明显,并且速率效应受球砾尺寸和板的弹性特性影响,呈现较强的相关性;球砾大小和速度相同时,等效弹性模量E*越大,法向恢复系数越小;含水状态对法向恢复系数影响不大。理论分析表明:P_(0,max)和k为控制法向恢复系数变化规律的内在因素;尺寸和速度均是通过改变P_(0,max)和k使法向恢复系数呈现复杂的尺寸效应和速率效应。
The normal restitution coefficient is a key parameter in the analysis of rockfall and its value determines directly the trajectory of rockfall. A device designed to simulate the collision process and the audio sampling technique was adopted in this paper in order to strictly measure the normal restitution coefficient of granite spheres and to analyze the influencing factors. The size of granite spheres,the elastic properties of plate,the impact velocity and the moisture state are considered to analyze the main influencing factors of the normal restitution coefficient. The maximum contact stress P_(0,max),the crack initiation velocity v_(ci) and the crack damage velocity v_(cd) are deduced based on the elastic contact theory. Moreover,the secant change rate of the contact stress is proposed to describe the rate-dependent collision process. Finally the size effect,the rate effect and the energy dissipation mechanism of the normal restitution coefficient are discussed. The experimental results show that the normal restitution coefficient of the granite spheres has strong size effect,which is more obvious under low velocity. The rate effect is also obvious and it is affected by the size of granite spheres and the elastic properties of the plate. The normal restitution coefficient reduces with the increasing of the equivalent elastic modulus E*. The moisture state has little effect on the restitution coefficient. The theoretical analysis shows that P_(0,max) and k are the main internal factors which influence the variation of the normal restitution coefficient. By changing P_(0,max) and k,the size of granite spheres and velocity make the normal restitution coefficient to show the complex size effect and rate effect.
The normal restitution coefficient is a key parameter in the analysis of rockfall and its value determines directly the trajectory of rockfall. A device designed to simulate the collision process and the audio sampling technique was adopted in this paper in order to strictly measure the normal restitution coefficient of granite spheres and to analyze the influencing factors. The size of granite spheres,the elastic properties of plate,the impact velocity and the moisture state are considered to analyze the main influencing factors of the normal restitution coefficient. The maximum contact stress P_(0,max),the crack initiation velocity v_(ci) and the crack damage velocity v_(cd) are deduced based on the elastic contact theory. Moreover,the secant change rate of the contact stress is proposed to describe the rate-dependent collision process. Finally the size effect,the rate effect and the energy dissipation mechanism of the normal restitution coefficient are discussed. The experimental results show that the normal restitution coefficient of the granite spheres has strong size effect,which is more obvious under low velocity. The rate effect is also obvious and it is affected by the size of granite spheres and the elastic properties of the plate. The normal restitution coefficient reduces with the increasing of the equivalent elastic modulus E*. The moisture state has little effect on the restitution coefficient. The theoretical analysis shows that P_(0,max) and k are the main internal factors which influence the variation of the normal restitution coefficient. By changing P_(0,max) and k,the size of granite spheres and velocity make the normal restitution coefficient to show the complex size effect and rate effect.
引文
[1]MACCIOTTA R,MARTIN C D,CRUDEN D M.Probabilistic estimation of rockfall height and kinetic energy based on a three-dimensional trajectory model and Monte Carlo simulation[J].Landslides,2015,12(4):757-772.
[2]LU Y E,ZHANG L M.Analysis of failure of a bridge foundation under rock impact[J].Acta Geotechnica,2012,7(1):57-68.
[3]CHAI B,TANG Z,ZHANG A,et al.An uncertainty method for probabilistic analysis of buildings impacted by rockfall in a limestone quarry in Fengshan,Southwestern China[J].Rock Mechanics and Rock Engineering,2015,48(5):1 981-1 996.
[4]CRUDEN M D,VARNES J D.Landslide types and processes.Landslides:investigation and mitigation,transportation research board[M].Washington,D.C:National Academy Press,1996:36-75.
[5]ANTONYUK S,HEINRICH S,TOMAS J,et al.Energy absorption during compression and impact of dry elastic-plastic spherical granules[J].Granular Matter,2010,12(1):15-47.
[6]章广成,向欣,唐辉明.落石碰撞恢复系数的现场试验与数值计算[J].岩石力学与工程学报,2011,30(6):1 266-1 273.(ZHANGGuangcheng,XIANG Xin,TANG Huiming.Field test and numerical calculation of restitution coefficient of rockfall collision[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(6):1 266-1 273.(in Chinese))
[7]DONG H K,GRATCHEV I,BERENDS J,et al.Calibration of restitution coefficients using rockfall simulations based on 3Dphotogrammetry model:a case study[J].Natural Hazards,2015,78(3):1 931-1 946.
[8]叶四桥,巩尚卿.落石碰撞法向恢复系数的模型试验研究[J].中国铁道科学,2015,36(4):13-19.(YE Siqiao,GONG Shangqing.Research on normal restitution coefficient of rockfall collision by model tests[J].China Railway Science,2015,36(4):13-19.(in Chinese))
[9]ASTERIOU P,SAROGLOU H,TSIAMBAOS G.Geotechnical and kinematic parameters affecting the coefficients of restitution for rock fall analysis[J].International Journal of Rock Mechanics and Mining Sciences,2012,54(3):103-113.
[10]BUZZI O,GIACOMINI A,SPADARI M.Laboratory investigation on high values of restitution coefficients[J].Rock Mechanics and Rock Engineering,2012,45(1):35-43.
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[13]HARP E L,DART R L,REICHENBACH P.Rock fall simulation at Timpanogos Cave National Monument,American Fork Canyon,Utah,USA[J].Landslides,2011,8(3):373-379.
[14]WANG X,FRATTINI P,CROSTA G B,et al.Uncertainty assessment in quantitative rockfall risk assessment[J].Landslides,2014,11(4):711-722.
[15]CUNDALL P A,STRACK O D L.A discrete numerical model for granular assemblies[J].Géotechnique,1979,29(1):331-336.
[16]何思明,吴永,李新坡.滚石冲击碰撞恢复系数研究[J].岩土力学,2009,30(3):623-627.(HE Siming,WU Yong,LI Xinpo.Research on restitution coefficient of rock fall[J].Rock and Soil Mechanics,2009,30(3):623-627.(in Chinese))
[17]钟文镇,何克晶,周照耀,等.颗粒离散元模拟中的阻尼系数标定[J].物理学报,2009,58(8):5 155-5 161.(ZHONG Wenzhen,HE Kejing,ZHOU Zhaoyao,et al.Calibration of damping coefficient in discrete element method simulation[J].Acta Physica Sinica,2009,58(8):5 155-5 161.(in Chinese))
[18]STRONGEW J.Impact mechanics[M].Cambridge:Cambridge University Press,2000:41-47.
[19]JOHNSON K L.Contact mechanics[M].徐秉业,罗学富,刘信声,等译.北京:高等教育出版社,1992:103-119.(JOHNSON K L.Contact mechanics[M].Translated by XU Bingye,LUO Xuefu,LIUXinsheng,et al.Beijing:Higher Education Press,1992:103-119.(in Chinese))
[20]LANDAU L D,LIFSCHITZ,E M.Theoretische Physik,Band VII:Elastizit?tstheorie[M].Moskau:Fizmatlit Press,2001:87-91.
[21]EBERHARDT E,STEAD D,STIMPSON B.Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression[J].International Journal of Rock Mechanics and Mining Sciences,1999,36(3):361-380.
[22]张春生,陈祥荣,侯靖,等.锦屏二级水电站深埋大理岩力学特性研究[J].岩石力学与工程学报,2010,10(10):1 999-2 009.(ZHANG Chunsheng,CHEN Xiangrong,HOU Jing,et al.Study of mechanical behavior of deep-buried marble at Jinping II hydropower station[J].Chinese Journal of Rock Mechanics and Engineering,2010,10(10):1 999-2 009.(in Chinese))
[23]赵星光,马利科,苏锐,等.北山深部花岗岩在压缩条件下的破裂演化与强度特性[J].岩石力学与工程学报,2014,33(增2):3 665-3 675.(ZHAO Xingguang,MA Like,SU Rui,et al.Fracture evolution and strength characteristics of Beishan deep granite under compression conditions[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(Supp.2):3 665-3 675.(in Chinese))
[24]周辉,孟凡震,张传庆,等.硬岩应力-应变门槛值特点及产生机制[J].岩石力学与工程学报,2015,34(8):1 513-1 521.(ZHOUHui,MENG Fanzhen,ZHANG Chuanqing,et al.Characteristics and mechanism of occurrence of stress thresholds and corresponding strain for hard rock[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(8):1 513-1 521.(in Chinese))
[25]黄书岭.高应力下脆性岩石的力学模型与工程应用研究[博士学位论文][D].武汉:武汉岩土力学研究所,2008.(HUANG Shuling.Study on mechanical model of brittle rock under high stress condition and its engineering applications[Ph.D.Thesis][D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2008.(in Chinese))
[26]MARTIN C D.Seventeenth canadian geotechnical colloquium:the effect of cohesion loss and stress path on brittle rock strength[J].Canadian Geotechnical Journal,1997,34(2):255-272.
[27]HARDY C,BARONET C N,TORDION G V.The elasto-plastic indentation of a half-space by a rigid sphere[J].International Journal for Numerical Methods in Engineering,1971,3(4):451-462.
[28]余寿文,冯西桥.损伤力学[M].北京:清华大学出版社,1997:26-28.(YU Shouwen,FENG Xiqiao.Damage mechanics[M].Beijing:Tsinghua University Press,1997:26-28.(in Chinese))
[29]谢和平,陈忠辉.岩石力学[M].北京:科学出版社,2004:213-214.(XIE Heping,CHENG Zhonghui.Rock mechanics[M].Beijing:Science Press,2004:213-214.(in Chinese))
[30]肖建清,冯夏庭,丁德馨,等.常幅循环荷载作用下岩石的滞后及阻尼效应研究[J].岩石力学与工程学报,2010,29(8):1 677-1 683.(XIAO Jianqing,FENG Xiating,DING Dexin,et al.Study of hysteresis and damping effects of rock subjected to constant amplitude cyclic loading[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(8):1 677-1 683.(in Chinese))
[31]戚承志,钱七虎.岩石等脆性材料动力强度依赖应变率的物理机制[J].岩石力学与工程学报,2003,22(2):177-181.(QI Chengzhi,QIAN Qihu.Physical mechanism of dependence of material strength on strain rate for rock-like material[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(2):177-181.(in Chinese))
[32]黎立云,徐志强,谢和平,等.不同冲击速度下岩石破坏能量规律的实验研究[J].煤炭学报,2011,36(12):2 007-2 011.(LI Liyun,XU Zhiqiang,XIE Heping,et al.Failure experimental study on energy laws of rock under differential dynamic impact velocities[J].Journal of China Coal Society,2011,36(12):2 007-2 011.(in Chinese))
[33]胡柳青,李夕兵,赵伏军.冲击荷载作用下岩石破裂损伤的耗能规律[J].岩石力学与工程学报,2002,21(增2):2 304-2 308.(HULiuqing,LI Xibing,ZHAO Fujun.Study on energy consumption in fracture and damage of rock induced by impact loadings[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(Supp.2):2 304-2 308.(in Chinese))
[34]CARMONA H A,WITTEL F K,KUN F,et al.Fragmentation processes in impact of spheres[J].Physical Review E,2008,77(5):463-470.
[35]戚承志,王明洋,钱七虎,等.冲击载作用下岩石变形破坏的细观结构特性[J].岩石力学与工程学报,2007,26(增1):3 367-3 372.(QI Chengzhi,WANG Mingyang,QIAN Qihu et al.Mesostructural aspects of deformation and fracture of rock under shock loading[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(Supp.1):3 367-3 372.(in Chinese))
[36]MORENO-ATANASIO R.Energy dissipation in agglomerates during normal impact[J].Powder Technology,2012,223(6):12-18.
[37]DMYTRO A,ELLIOTT J A,HANCOCK B C.Effect of particle size on energy dissipation in viscoelastic granular collisions[J].Physical Review E Statistical Nonlinear and Soft Matter Physics,2011,84(1):1 713-1 724.
[38]KUWABARA G,KONO K.Restitution coefficient in a collision between two spheres[J].Japanese Journal of Applied Physics,1987,26(8):1 230-1 233.
[39]BRILLIANTOV N V,SPAHN F,HERTZSCH J M,et al.Model for collisions in granular gases[J].Phys.rev.e,1996,53(5):5 382.
[40]ALIZADEH E,BERTRAND F,CHAOUKI J.Development of a granular normal contact force model based on a non-Newtonian liquid filled dashpot[J].Powder Technology,2013,237(3):202-212.
[41]FU J,ADAMS M J,REYNOLDS G K,et al.Impact deformation and rebound of wet granules[J].Powder Technology,2004,140(3):248-257.
[42]FU J S,CHEONG Y S,REYNOLDS G K,et al.An experimental study of the variability in the properties and quality of wet granules[J].Powder Technology,2004,140(3):209-216.
[2]LU Y E,ZHANG L M.Analysis of failure of a bridge foundation under rock impact[J].Acta Geotechnica,2012,7(1):57-68.
[3]CHAI B,TANG Z,ZHANG A,et al.An uncertainty method for probabilistic analysis of buildings impacted by rockfall in a limestone quarry in Fengshan,Southwestern China[J].Rock Mechanics and Rock Engineering,2015,48(5):1 981-1 996.
[4]CRUDEN M D,VARNES J D.Landslide types and processes.Landslides:investigation and mitigation,transportation research board[M].Washington,D.C:National Academy Press,1996:36-75.
[5]ANTONYUK S,HEINRICH S,TOMAS J,et al.Energy absorption during compression and impact of dry elastic-plastic spherical granules[J].Granular Matter,2010,12(1):15-47.
[6]章广成,向欣,唐辉明.落石碰撞恢复系数的现场试验与数值计算[J].岩石力学与工程学报,2011,30(6):1 266-1 273.(ZHANGGuangcheng,XIANG Xin,TANG Huiming.Field test and numerical calculation of restitution coefficient of rockfall collision[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(6):1 266-1 273.(in Chinese))
[7]DONG H K,GRATCHEV I,BERENDS J,et al.Calibration of restitution coefficients using rockfall simulations based on 3Dphotogrammetry model:a case study[J].Natural Hazards,2015,78(3):1 931-1 946.
[8]叶四桥,巩尚卿.落石碰撞法向恢复系数的模型试验研究[J].中国铁道科学,2015,36(4):13-19.(YE Siqiao,GONG Shangqing.Research on normal restitution coefficient of rockfall collision by model tests[J].China Railway Science,2015,36(4):13-19.(in Chinese))
[9]ASTERIOU P,SAROGLOU H,TSIAMBAOS G.Geotechnical and kinematic parameters affecting the coefficients of restitution for rock fall analysis[J].International Journal of Rock Mechanics and Mining Sciences,2012,54(3):103-113.
[10]BUZZI O,GIACOMINI A,SPADARI M.Laboratory investigation on high values of restitution coefficients[J].Rock Mechanics and Rock Engineering,2012,45(1):35-43.
[11]RITCHIE A M.Evaluation of rockfall and its control[J].Highway Research Record,1963,17(1):13-28.
[12]GIGLI G,MORELLI S,FORNERA S,et al.Terrestrial laser scanner and geomechanical surveys for the rapid evaluation of rock fall susceptibility scenarios[J].Landslides,2014,11(1):1-14.
[13]HARP E L,DART R L,REICHENBACH P.Rock fall simulation at Timpanogos Cave National Monument,American Fork Canyon,Utah,USA[J].Landslides,2011,8(3):373-379.
[14]WANG X,FRATTINI P,CROSTA G B,et al.Uncertainty assessment in quantitative rockfall risk assessment[J].Landslides,2014,11(4):711-722.
[15]CUNDALL P A,STRACK O D L.A discrete numerical model for granular assemblies[J].Géotechnique,1979,29(1):331-336.
[16]何思明,吴永,李新坡.滚石冲击碰撞恢复系数研究[J].岩土力学,2009,30(3):623-627.(HE Siming,WU Yong,LI Xinpo.Research on restitution coefficient of rock fall[J].Rock and Soil Mechanics,2009,30(3):623-627.(in Chinese))
[17]钟文镇,何克晶,周照耀,等.颗粒离散元模拟中的阻尼系数标定[J].物理学报,2009,58(8):5 155-5 161.(ZHONG Wenzhen,HE Kejing,ZHOU Zhaoyao,et al.Calibration of damping coefficient in discrete element method simulation[J].Acta Physica Sinica,2009,58(8):5 155-5 161.(in Chinese))
[18]STRONGEW J.Impact mechanics[M].Cambridge:Cambridge University Press,2000:41-47.
[19]JOHNSON K L.Contact mechanics[M].徐秉业,罗学富,刘信声,等译.北京:高等教育出版社,1992:103-119.(JOHNSON K L.Contact mechanics[M].Translated by XU Bingye,LUO Xuefu,LIUXinsheng,et al.Beijing:Higher Education Press,1992:103-119.(in Chinese))
[20]LANDAU L D,LIFSCHITZ,E M.Theoretische Physik,Band VII:Elastizit?tstheorie[M].Moskau:Fizmatlit Press,2001:87-91.
[21]EBERHARDT E,STEAD D,STIMPSON B.Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression[J].International Journal of Rock Mechanics and Mining Sciences,1999,36(3):361-380.
[22]张春生,陈祥荣,侯靖,等.锦屏二级水电站深埋大理岩力学特性研究[J].岩石力学与工程学报,2010,10(10):1 999-2 009.(ZHANG Chunsheng,CHEN Xiangrong,HOU Jing,et al.Study of mechanical behavior of deep-buried marble at Jinping II hydropower station[J].Chinese Journal of Rock Mechanics and Engineering,2010,10(10):1 999-2 009.(in Chinese))
[23]赵星光,马利科,苏锐,等.北山深部花岗岩在压缩条件下的破裂演化与强度特性[J].岩石力学与工程学报,2014,33(增2):3 665-3 675.(ZHAO Xingguang,MA Like,SU Rui,et al.Fracture evolution and strength characteristics of Beishan deep granite under compression conditions[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(Supp.2):3 665-3 675.(in Chinese))
[24]周辉,孟凡震,张传庆,等.硬岩应力-应变门槛值特点及产生机制[J].岩石力学与工程学报,2015,34(8):1 513-1 521.(ZHOUHui,MENG Fanzhen,ZHANG Chuanqing,et al.Characteristics and mechanism of occurrence of stress thresholds and corresponding strain for hard rock[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(8):1 513-1 521.(in Chinese))
[25]黄书岭.高应力下脆性岩石的力学模型与工程应用研究[博士学位论文][D].武汉:武汉岩土力学研究所,2008.(HUANG Shuling.Study on mechanical model of brittle rock under high stress condition and its engineering applications[Ph.D.Thesis][D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2008.(in Chinese))
[26]MARTIN C D.Seventeenth canadian geotechnical colloquium:the effect of cohesion loss and stress path on brittle rock strength[J].Canadian Geotechnical Journal,1997,34(2):255-272.
[27]HARDY C,BARONET C N,TORDION G V.The elasto-plastic indentation of a half-space by a rigid sphere[J].International Journal for Numerical Methods in Engineering,1971,3(4):451-462.
[28]余寿文,冯西桥.损伤力学[M].北京:清华大学出版社,1997:26-28.(YU Shouwen,FENG Xiqiao.Damage mechanics[M].Beijing:Tsinghua University Press,1997:26-28.(in Chinese))
[29]谢和平,陈忠辉.岩石力学[M].北京:科学出版社,2004:213-214.(XIE Heping,CHENG Zhonghui.Rock mechanics[M].Beijing:Science Press,2004:213-214.(in Chinese))
[30]肖建清,冯夏庭,丁德馨,等.常幅循环荷载作用下岩石的滞后及阻尼效应研究[J].岩石力学与工程学报,2010,29(8):1 677-1 683.(XIAO Jianqing,FENG Xiating,DING Dexin,et al.Study of hysteresis and damping effects of rock subjected to constant amplitude cyclic loading[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(8):1 677-1 683.(in Chinese))
[31]戚承志,钱七虎.岩石等脆性材料动力强度依赖应变率的物理机制[J].岩石力学与工程学报,2003,22(2):177-181.(QI Chengzhi,QIAN Qihu.Physical mechanism of dependence of material strength on strain rate for rock-like material[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(2):177-181.(in Chinese))
[32]黎立云,徐志强,谢和平,等.不同冲击速度下岩石破坏能量规律的实验研究[J].煤炭学报,2011,36(12):2 007-2 011.(LI Liyun,XU Zhiqiang,XIE Heping,et al.Failure experimental study on energy laws of rock under differential dynamic impact velocities[J].Journal of China Coal Society,2011,36(12):2 007-2 011.(in Chinese))
[33]胡柳青,李夕兵,赵伏军.冲击荷载作用下岩石破裂损伤的耗能规律[J].岩石力学与工程学报,2002,21(增2):2 304-2 308.(HULiuqing,LI Xibing,ZHAO Fujun.Study on energy consumption in fracture and damage of rock induced by impact loadings[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(Supp.2):2 304-2 308.(in Chinese))
[34]CARMONA H A,WITTEL F K,KUN F,et al.Fragmentation processes in impact of spheres[J].Physical Review E,2008,77(5):463-470.
[35]戚承志,王明洋,钱七虎,等.冲击载作用下岩石变形破坏的细观结构特性[J].岩石力学与工程学报,2007,26(增1):3 367-3 372.(QI Chengzhi,WANG Mingyang,QIAN Qihu et al.Mesostructural aspects of deformation and fracture of rock under shock loading[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(Supp.1):3 367-3 372.(in Chinese))
[36]MORENO-ATANASIO R.Energy dissipation in agglomerates during normal impact[J].Powder Technology,2012,223(6):12-18.
[37]DMYTRO A,ELLIOTT J A,HANCOCK B C.Effect of particle size on energy dissipation in viscoelastic granular collisions[J].Physical Review E Statistical Nonlinear and Soft Matter Physics,2011,84(1):1 713-1 724.
[38]KUWABARA G,KONO K.Restitution coefficient in a collision between two spheres[J].Japanese Journal of Applied Physics,1987,26(8):1 230-1 233.
[39]BRILLIANTOV N V,SPAHN F,HERTZSCH J M,et al.Model for collisions in granular gases[J].Phys.rev.e,1996,53(5):5 382.
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