基于弹塑性理论的落石碰撞恢复系数和峰值冲击力研究
|
摘要
考虑土体的弹塑性特征,利用经典接触理论,假设在法向与切向相互独立的基础上,根据入射条件,提出了一种计算切向力的新模型。推导了落石碰撞过程中的能量恢复系数和冲击力的计算公式;得到以初始入射速度和入射角为变参量下的恢复系数和冲击力的变化规律。结果表明:当入射速度相同时,恢复系数与入射角呈正相关;当冲击入射角相同时,恢复系数与速度呈负相关,而冲击力与速度呈线性正相关;落石回弹的运动状态取决于初始入射条件,通过坡面条件及入射条件对可能掉落的危岩体进行运动形态的判别;目前普遍采用的Thornton速度恢复系数偏大,会造成防护结构的失效或材料浪费。
Considering the elastic-plastic characteristics of soils and using the classical contact theory, a new model for calculating the tangential force was proposed based on the incident conditions. The calculation formula of the energy coefficient of restitution and impact force during the collision process was deduced. And the change rule of the coefficient of restitution and the impact force under the initial incident rate and the incident angle were obtained. The results show that when the incident velocity is the same, the coefficient of restitution is positively correlated with the incident angle. When the impact angle is the same, the coefficient of restitution is negatively correlated with the velocity, and the impact force is linearly related to the velocity. The movement state of the rockfall depends on the initial incidence conditions. Through the slope conditions and the incident conditions on the possible decline of the dangerous rock body, the form of movement was determined. The current commonly used Thornton coefficient of restitution of speed is too large, and will cause the failure of the protective structure or material waste.
Considering the elastic-plastic characteristics of soils and using the classical contact theory, a new model for calculating the tangential force was proposed based on the incident conditions. The calculation formula of the energy coefficient of restitution and impact force during the collision process was deduced. And the change rule of the coefficient of restitution and the impact force under the initial incident rate and the incident angle were obtained. The results show that when the incident velocity is the same, the coefficient of restitution is positively correlated with the incident angle. When the impact angle is the same, the coefficient of restitution is negatively correlated with the velocity, and the impact force is linearly related to the velocity. The movement state of the rockfall depends on the initial incidence conditions. Through the slope conditions and the incident conditions on the possible decline of the dangerous rock body, the form of movement was determined. The current commonly used Thornton coefficient of restitution of speed is too large, and will cause the failure of the protective structure or material waste.
引文
[1]WHALLEY W B.Slope stability[M].New York:Wiley,1984.
[2]GLOVER J,BARTELT P,CHRISTEN M,et al.Rockfallsimulation with irregular rock blocks[M]∥Engineering Geology for Society and Territory.Cham:Springer,2015.
[3]RITCHIE A M.Evaluation of rockfall and its control[J].Journal of Experimental Psychology Applied,1963,2(4):291-304.
[4]ROCHET L.Application des modeles numeriques de propagation a l'etude des eboulement srocheux[M].Champs-Sur-Marne:Bull Liaison Lab Ponts Chauss,1987.
[5]张路青,杨志法.公路沿线遭遇落石的风险分析-案例研究[J].岩石力学与工程学报,2004,23(21):3700-3708.ZHANG Luqing,YANG Zhifa.Risk analysis of encountering rockfalls on a highway-a case study[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(21):3700-3708.
[6]JR J F S,BISHOP M P.Mass movement in the Himalaya:new insights and research directions[J].Geomorphology,1998,26(1/2/3):13-35.
[7]DHAKAL S,KHAREL P.Hazard rating and event tree analysis for assessing rockfall risks along Siddhartha Highway in Siddhababa Area,Nepal[J].International Journal of Landslide and Environment,2013,1(1):41-42.
[8]UPRETI B,DHITAL M.Landslide studies and management in Nepal[R].Kathmandu:International Center for Integrated Mountain Development(ICIMOD),1996.
[9]PARONUZZI P.Field evidence and kinematical backanalysis of block rebounds:the lavone rockfall,northern italy[J].Rock Mechanics and Rock Engineering,2009,42(5):783-813.
[10]PROCTER E,STRAPAZZON G,BALKENHOL K,et al.Search and rescue response to a large-scale rockfall disaster[J].Wilderness&Environmental Medicine,2015,26(1):68-71.
[11]GARDNER J.Rockfall:a geomorphic process in high mountain terrain[J].Albertan Geographer,1970,6:15-20.
[12]YAMAGISHI H.Recent landslides in western Hokkaido,Japan[J].Pure&Applied Geophysics,2000,157(6/7/8):1115-1134.
[13]KOJAN E,HUTCHINSON J N.Mayunmarca rockslide and debris flow,peru[J].Developments in Geotechnical Engineering,1978,14:315-361.
[14]ASTERIOU P,SAROGLOU H,TSIAMBAOS G.Rockfall:scaling factors for the coefficient of restitution[C]∥Eurock2013 Rock Mechanics for Resources,Energy&Environment.Wroclaw:RMREE,2013.
[15]LABIOUSE V,HEIDENREICH B.Half-scale experimental study of rockfall impacts on sandy slopes[J].Natural Hazards&Earth System Sciences,2009,9(6):1981-1993.
[16]PEILA D,OGGERI C,CASTIGLIA C.Ground reinforced embankments for rockfall protection:design and evaluation of full scale tests[J].Landslides,2007,4(3):255-265.
[17]RONCO C,OGGERI C,PEILA D.Design of reinforced ground embankments used for rockfall protection[J].Natural Hazards&Earth System Sciences,2009,9(4):1189-1199.
[18]ASTERIOU P,TSIAMBAOS G.Empirical model for predicting rockfall trajectory direction[J].Rock Mechanics&Rock Engineering,2015,49(3):1-15.
[19]CHAU K T,WONG R H C,WU J J.Coefficient of restitution and rotational motions of rockfall impacts[J].International Journal of Rock Mechanics&Mining Sciences,2002,39(1):69-77.
[20]袁进科,黄润秋,裴向军.滚石冲击力测试研究[J].岩土力学,2014,35(1):48-54.YUAN Jinke,HUANG Runqiu,PEI Xiangjun.Test research on rockfall impact force[J].Rock and Soil Mechanics,2014,35(1):48-54.
[21]杨海清,周小平.边坡落石运动轨迹计算新方法[J].岩土力学,2009,30(11):3411-3416.YANG Haiqing,ZHOU Xiaoping.A new approach to calculate trajectory of rockfall[J].Rock and Soil Mechanics,2009,30(11):3411-3416.
[22]何思明.落石对防护结构的冲击压力计算[J].工程力学,2010,27(9):175-180.HE Siming.Calculation of compact pressure of rockfall on shield structures[J].Engineering Mechanics,2010,27(9):175-180.
[23]王东坡,何思明,吴永,等.滚石防护棚洞EPS垫层结构缓冲作用研究[J].振动与冲击,2014,33(4):199-203.WANG Dongpo,HE Siming,WU Yong,et al.Cushioning effect of rock sheds with EPS cushion on rock-falls action[J].Journal of Vibration and Shock,2014,33(4):199-203.
[24]王爽,周晓军,罗福君,等.拱形棚洞受落石冲击的模型试验研究[J].振动与冲击,2017,36(12):215-222.WANG Shuang,ZHOU Xiaojun,LUO Fujun,et al.An experimental study on the performance of an arch shaped shed tunnel due to the impact of rockfall[J].Journal of Vibration and Shock,2017,36(12):215-222.
[25]PARONUZZI P.Field evidence and kinematical back-analysis of block rebounds:the lavone rockfall,northern italy[J].Rock Mechanics&Rock Engineering,2009,42(5):783-813.
[26]SPADARI M,GIACOMINI A,BUZZI O,et al.In situ rockfall testing in new south wales,australia[J].International Journal of Rock Mechanics&Mining Sciences,2012,49(2):84-93.
[27]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.
[28]陈宇龙.滚石运动过程中关键参数的影响分析[J].岩土工程学报,2013,35(增刊2):191-196.CHEN Yulong.Influence of key factors on trajectories of rockfalls[J].Chinese Journal of Geotechnical Engineering,2013,35(Sup2):191-196.
[29]JOHNSON K L.接触力学[M].徐秉业,罗学富,译.北京:高等教育出版社,1992.
[30]JACKSON R L,GREEN I.A finite element study of elastoplastic hemispherical contact[J].Journal of Tribology,2005,127(2):343-354.
[31]JACKSON R L,GREEN I,DAN B M.Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres[J].Nonlinear Dynamics,2010,60(3):217-229.
[32]KLIGERMAN Y,ETSION I,KADIN,Y.Unloading of an elastic-plastic loaded spherical contact[J].International Journal of Solids and Structures,2005,42(13):3716-3729.
[33]MINDLIN R D.Compliance of elastic bodies in contact,ASME[J].Journal of Applied Mechanics,1949(16):259-268.
[34]VU-QUOC L,LESBURG L,ZHANG X.An accurate tangential force-displacement model for granular-flow simulations:contacting spheres with plastic deformation,force-driven formulation[J].Journal of Computational Physics,2004,196(1):298-326.
[35]何思明,吴永,李新坡.落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.
[36]FUJIMOTO T,KAGAMI J,KAWAGUCHI T,et al.Microdisplacement characteristics under tangential force[J].Wear,2000,241(2):136-142.
[37]MAW N,BARBER J R,FAWCETT J N.The oblique impact of elastic spheres[J].Wear,1976,38(1):101-111.
[38]KHARAZ A H,GORHAM D A,SALMAN A D.An experimental study of the elastic rebound of spheres[J].Powder Technology,2001,120(3):281-291.
[39]何思明,李新坡,吴永.落石冲击荷载作用下土体屈服特性研究[J].岩石力学与工程学报,2008,27(增刊1):2973-2977.HE Siming.Study on incipient yield property of soil under rock-fall impact[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(Sup1):2973-2977.
[40]陈洪凯,唐红梅,王林峰.危岩崩塌演化理论及应用[M].北京:科学出版社,2009.
[41]KAWAHARA S,MURO T.Effects of dry density and thickness of sandy soil on impact response due to rockfall[J].Journal of Terramechanics,2006,43(3):329-340.
[2]GLOVER J,BARTELT P,CHRISTEN M,et al.Rockfallsimulation with irregular rock blocks[M]∥Engineering Geology for Society and Territory.Cham:Springer,2015.
[3]RITCHIE A M.Evaluation of rockfall and its control[J].Journal of Experimental Psychology Applied,1963,2(4):291-304.
[4]ROCHET L.Application des modeles numeriques de propagation a l'etude des eboulement srocheux[M].Champs-Sur-Marne:Bull Liaison Lab Ponts Chauss,1987.
[5]张路青,杨志法.公路沿线遭遇落石的风险分析-案例研究[J].岩石力学与工程学报,2004,23(21):3700-3708.ZHANG Luqing,YANG Zhifa.Risk analysis of encountering rockfalls on a highway-a case study[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(21):3700-3708.
[6]JR J F S,BISHOP M P.Mass movement in the Himalaya:new insights and research directions[J].Geomorphology,1998,26(1/2/3):13-35.
[7]DHAKAL S,KHAREL P.Hazard rating and event tree analysis for assessing rockfall risks along Siddhartha Highway in Siddhababa Area,Nepal[J].International Journal of Landslide and Environment,2013,1(1):41-42.
[8]UPRETI B,DHITAL M.Landslide studies and management in Nepal[R].Kathmandu:International Center for Integrated Mountain Development(ICIMOD),1996.
[9]PARONUZZI P.Field evidence and kinematical backanalysis of block rebounds:the lavone rockfall,northern italy[J].Rock Mechanics and Rock Engineering,2009,42(5):783-813.
[10]PROCTER E,STRAPAZZON G,BALKENHOL K,et al.Search and rescue response to a large-scale rockfall disaster[J].Wilderness&Environmental Medicine,2015,26(1):68-71.
[11]GARDNER J.Rockfall:a geomorphic process in high mountain terrain[J].Albertan Geographer,1970,6:15-20.
[12]YAMAGISHI H.Recent landslides in western Hokkaido,Japan[J].Pure&Applied Geophysics,2000,157(6/7/8):1115-1134.
[13]KOJAN E,HUTCHINSON J N.Mayunmarca rockslide and debris flow,peru[J].Developments in Geotechnical Engineering,1978,14:315-361.
[14]ASTERIOU P,SAROGLOU H,TSIAMBAOS G.Rockfall:scaling factors for the coefficient of restitution[C]∥Eurock2013 Rock Mechanics for Resources,Energy&Environment.Wroclaw:RMREE,2013.
[15]LABIOUSE V,HEIDENREICH B.Half-scale experimental study of rockfall impacts on sandy slopes[J].Natural Hazards&Earth System Sciences,2009,9(6):1981-1993.
[16]PEILA D,OGGERI C,CASTIGLIA C.Ground reinforced embankments for rockfall protection:design and evaluation of full scale tests[J].Landslides,2007,4(3):255-265.
[17]RONCO C,OGGERI C,PEILA D.Design of reinforced ground embankments used for rockfall protection[J].Natural Hazards&Earth System Sciences,2009,9(4):1189-1199.
[18]ASTERIOU P,TSIAMBAOS G.Empirical model for predicting rockfall trajectory direction[J].Rock Mechanics&Rock Engineering,2015,49(3):1-15.
[19]CHAU K T,WONG R H C,WU J J.Coefficient of restitution and rotational motions of rockfall impacts[J].International Journal of Rock Mechanics&Mining Sciences,2002,39(1):69-77.
[20]袁进科,黄润秋,裴向军.滚石冲击力测试研究[J].岩土力学,2014,35(1):48-54.YUAN Jinke,HUANG Runqiu,PEI Xiangjun.Test research on rockfall impact force[J].Rock and Soil Mechanics,2014,35(1):48-54.
[21]杨海清,周小平.边坡落石运动轨迹计算新方法[J].岩土力学,2009,30(11):3411-3416.YANG Haiqing,ZHOU Xiaoping.A new approach to calculate trajectory of rockfall[J].Rock and Soil Mechanics,2009,30(11):3411-3416.
[22]何思明.落石对防护结构的冲击压力计算[J].工程力学,2010,27(9):175-180.HE Siming.Calculation of compact pressure of rockfall on shield structures[J].Engineering Mechanics,2010,27(9):175-180.
[23]王东坡,何思明,吴永,等.滚石防护棚洞EPS垫层结构缓冲作用研究[J].振动与冲击,2014,33(4):199-203.WANG Dongpo,HE Siming,WU Yong,et al.Cushioning effect of rock sheds with EPS cushion on rock-falls action[J].Journal of Vibration and Shock,2014,33(4):199-203.
[24]王爽,周晓军,罗福君,等.拱形棚洞受落石冲击的模型试验研究[J].振动与冲击,2017,36(12):215-222.WANG Shuang,ZHOU Xiaojun,LUO Fujun,et al.An experimental study on the performance of an arch shaped shed tunnel due to the impact of rockfall[J].Journal of Vibration and Shock,2017,36(12):215-222.
[25]PARONUZZI P.Field evidence and kinematical back-analysis of block rebounds:the lavone rockfall,northern italy[J].Rock Mechanics&Rock Engineering,2009,42(5):783-813.
[26]SPADARI M,GIACOMINI A,BUZZI O,et al.In situ rockfall testing in new south wales,australia[J].International Journal of Rock Mechanics&Mining Sciences,2012,49(2):84-93.
[27]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.
[28]陈宇龙.滚石运动过程中关键参数的影响分析[J].岩土工程学报,2013,35(增刊2):191-196.CHEN Yulong.Influence of key factors on trajectories of rockfalls[J].Chinese Journal of Geotechnical Engineering,2013,35(Sup2):191-196.
[29]JOHNSON K L.接触力学[M].徐秉业,罗学富,译.北京:高等教育出版社,1992.
[30]JACKSON R L,GREEN I.A finite element study of elastoplastic hemispherical contact[J].Journal of Tribology,2005,127(2):343-354.
[31]JACKSON R L,GREEN I,DAN B M.Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres[J].Nonlinear Dynamics,2010,60(3):217-229.
[32]KLIGERMAN Y,ETSION I,KADIN,Y.Unloading of an elastic-plastic loaded spherical contact[J].International Journal of Solids and Structures,2005,42(13):3716-3729.
[33]MINDLIN R D.Compliance of elastic bodies in contact,ASME[J].Journal of Applied Mechanics,1949(16):259-268.
[34]VU-QUOC L,LESBURG L,ZHANG X.An accurate tangential force-displacement model for granular-flow simulations:contacting spheres with plastic deformation,force-driven formulation[J].Journal of Computational Physics,2004,196(1):298-326.
[35]何思明,吴永,李新坡.落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.
[36]FUJIMOTO T,KAGAMI J,KAWAGUCHI T,et al.Microdisplacement characteristics under tangential force[J].Wear,2000,241(2):136-142.
[37]MAW N,BARBER J R,FAWCETT J N.The oblique impact of elastic spheres[J].Wear,1976,38(1):101-111.
[38]KHARAZ A H,GORHAM D A,SALMAN A D.An experimental study of the elastic rebound of spheres[J].Powder Technology,2001,120(3):281-291.
[39]何思明,李新坡,吴永.落石冲击荷载作用下土体屈服特性研究[J].岩石力学与工程学报,2008,27(增刊1):2973-2977.HE Siming.Study on incipient yield property of soil under rock-fall impact[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(Sup1):2973-2977.
[40]陈洪凯,唐红梅,王林峰.危岩崩塌演化理论及应用[M].北京:科学出版社,2009.
[41]KAWAHARA S,MURO T.Effects of dry density and thickness of sandy soil on impact response due to rockfall[J].Journal of Terramechanics,2006,43(3):329-340.