考虑微凸体曲率半径变化的GW改进模型
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摘要
经典的GW(Greenwood和Williamson)模型假设微凸体均为弹性,并没有考虑到微凸体磨损后曲率半径变化的情况。在经典赫兹接触理论与GW模型基础上推导出微凸体曲率为定值时的摩擦面剪切刚度公式。根据Mohr-Coulomb准则探讨了单个微凸体在法向压力与切向摩擦力作用下的屈服点位置,推导出单个微凸体所能承受的临界压力公式,由临界压力公式发现压力与微凸体曲率半径一一对应。提出一个考虑微凸体磨损的摩擦模型,结合单个微凸体临界压力公式与微凸体为定值时的摩擦面剪切刚度公式,得出了考虑微凸体曲率半径变化的摩擦面剪切刚度公式。该模型计算结果真实反映了试验情况:对于确定粗糙度的岩石表面,随着压力增加岩石表面逐渐变平缓;对于不同粗糙度岩石表面,随着粗糙度增加岩石表面更容易被磨平。
The classical Greenwood and Williamson( GW) model assumes that the asperity is elastic,which does not take into account the changes of curvature radius of the asperity after wearing. On the basis of classical Hertz contact theory and GW model,the shear stiffness formula of the friction surface was derived when the asperity curvature is constant. According to the Mohr-Coulomb criterion,the yield point position of a single asperity under normal pressure and tangential friction force was discussed. And the critical pressure formula for a single asperity was derived,which showed that the pressure corresponds to the radius of curvature of asperity. A model considering the wear of asperities was proposed and the shear stiffness formula of the friction surface considering the changes of the curvature of the asperity was obtained by combining the shear stiffness formula with a constant curvature radius and the critical pressure formula for a single asperity. The calculation results of the model are in a good agreement with the test results. For the specific roughness of rock surface,with the increase of pressure,the rock surface gradually becomes smooth; for different roughness of rock surface,with the increase of roughness,the rock surface is easier to be smoothed.
The classical Greenwood and Williamson( GW) model assumes that the asperity is elastic,which does not take into account the changes of curvature radius of the asperity after wearing. On the basis of classical Hertz contact theory and GW model,the shear stiffness formula of the friction surface was derived when the asperity curvature is constant. According to the Mohr-Coulomb criterion,the yield point position of a single asperity under normal pressure and tangential friction force was discussed. And the critical pressure formula for a single asperity was derived,which showed that the pressure corresponds to the radius of curvature of asperity. A model considering the wear of asperities was proposed and the shear stiffness formula of the friction surface considering the changes of the curvature of the asperity was obtained by combining the shear stiffness formula with a constant curvature radius and the critical pressure formula for a single asperity. The calculation results of the model are in a good agreement with the test results. For the specific roughness of rock surface,with the increase of pressure,the rock surface gradually becomes smooth; for different roughness of rock surface,with the increase of roughness,the rock surface is easier to be smoothed.
引文
[1]Wang W L,Wang T T,Su J J,et al.Assessment of damage in mountain tunnels due to the Taiwan Chi-Chi Earthquake[J].Tunnelling&Underground Space Technology Incorporating Trenchless Technology Research,2001,16(3):133-150.
[2]Rodríguez C E,Bommer J J,Chandler R J.Earthquakeinduced landslides:1980—1997[J].Soil Dynamics&Earthquake Engineering,1999,18(5):325-346.
[3]谢和平,陈忠辉,周宏伟,等.基于工程体与地质体相互作用的两体力学模型初探[J].岩石力学与工程学报,2005,24(9):1457-1464.Xie Heping,Chen Zhonghui,Zhou Hongwei,et al.Study on two-body mechanical model based on interaction between structural body and geo-body[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(9):1457-1464.
[4]谢和平,陈忠辉,易成,等.基于工程体-地质体相互作用的接触面变形破坏研究[J].岩石力学与工程学报,2008,27(9):1767-1780.Xie Heping,Chen Zhonghui,Yi Cheng,et al.Research on deformation and failure of interface based on interaction between structural body and geo-body[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(9):1767-1780.
[5]Scholz C H.Earthquakes and friction laws[J].Nature,1998,391:37-42.
[6]Matsu'Ura M,Kataoka H,Shibazaki B.Slip-dependent friction law and nucleation processes in earthquake rupture[J].Tectonophysics,1992,211(1/4):135-148.
[7]Ruiz S,Madariaga R.Determination of the friction law parameters of the Mw 6.7 Michilla earthquake in northern Chile by dynamic inversion[J].Geophysical Research Letters,2011,38(9):199-208.
[8]Ide S.Dynamic rupture propagation on a 2D fault with fractal frictional properties[J].Earth Planets&Space,2007,59(10):1099-1109.
[9]Maksimovic'M.New description of the shear strength for rock joints[J].Rock Mechanics&Rock Engineering,1992,25(4):275-284.
[10]Ladanyi B,Archambault G.Simulation of shear behavior of a jointed rock mass[J].US.Symposium on Rock Mechanics,1969,20(11):59-65.
[11]Barton N.Review of a new shear-strength criterion for rock joints[J].Engineering Geology,1973,7(4):287-332.
[12]沈明荣,张清照.规则齿型结构面剪切特性的模型试验研究[J].岩石力学与工程学报,2010,29(4):713-719.Shen Mingrong,Zhang Qingzhao.Experimental study of shear deformation characteristics of rock mass discontinuities[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(4):713-719.
[13]Qi C,Wang M,Bai J,et al.Investigation into size and strain rate effects on the strength of rock-like materials[J].International Journal of Rock Mechanics and Mining Sciences,2016,86:132-140.
[14]张学良,温椒花.基于接触分形理论的结合面切向接触刚度分形模型[J].农业机械学报,2002,33(3):91-93.Zhang Xueliang,Weng Jiaohua.A fractal model of tangential contact stiffness of joint surfaces based on the contact fractal theory[J].Transactions of the Chinese Society of Agricultural Machinery,2002,33(3):91-93.
[15]易成,王长军,张亮,等.基于两体相互作用问题的粗糙表面形貌描述指标系统的研究[J].岩石力学与工程学报,2006,25(12):2481-2492.Yi Cheng,Wang Changjun,Zhang Liang,et al.Study on description index system of rough surface based on bibody interaction[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(12):2481-2492.
[16]Jing L.Numerical modelling of jointed rock masses by Distinct Element Method for two and three-dimensional problems[D].Sweden,Lulea:Lulea University of Technology,1990.
[17]Jing L,Stephansson O,Nordlund E.Study of rock joints under cyclic loading conditions[J].Rock Mechanics&Rock Engineering,1993,26(3):215-232.
[18]Greenwood J A,Williamson J B P.Contact of nominally flat surfaces[J].Proceedings of the Royal Society of London,1966,295(1442):300-319.
[19]Popov V L.接触力学与摩擦学的原理及其应用[M].李强,雒建斌,译.北京:清华大学出版社,2011.
[20]Hamilton G M.Explicit equations for the stresses beneath a sliding spherical contact[J].Archive Proceedings of the Institution of Mechanical Engineers,1983,197(1):53-59.
[21]赵超,钟新谷,刘波,等.基于刚体弹簧法的钢筋混凝土结构破坏过程模拟方法[J].矿业科学学报,2018,3(2):129-138.Zhao Chao,Zhong Xingu,Liu Bo,et al.Numerical simulation of the failure process of reinforced concrete structures based on the rigid body spring method[J].Journal of Mining Science and Technology,2018,3(2):129-138.
[2]Rodríguez C E,Bommer J J,Chandler R J.Earthquakeinduced landslides:1980—1997[J].Soil Dynamics&Earthquake Engineering,1999,18(5):325-346.
[3]谢和平,陈忠辉,周宏伟,等.基于工程体与地质体相互作用的两体力学模型初探[J].岩石力学与工程学报,2005,24(9):1457-1464.Xie Heping,Chen Zhonghui,Zhou Hongwei,et al.Study on two-body mechanical model based on interaction between structural body and geo-body[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(9):1457-1464.
[4]谢和平,陈忠辉,易成,等.基于工程体-地质体相互作用的接触面变形破坏研究[J].岩石力学与工程学报,2008,27(9):1767-1780.Xie Heping,Chen Zhonghui,Yi Cheng,et al.Research on deformation and failure of interface based on interaction between structural body and geo-body[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(9):1767-1780.
[5]Scholz C H.Earthquakes and friction laws[J].Nature,1998,391:37-42.
[6]Matsu'Ura M,Kataoka H,Shibazaki B.Slip-dependent friction law and nucleation processes in earthquake rupture[J].Tectonophysics,1992,211(1/4):135-148.
[7]Ruiz S,Madariaga R.Determination of the friction law parameters of the Mw 6.7 Michilla earthquake in northern Chile by dynamic inversion[J].Geophysical Research Letters,2011,38(9):199-208.
[8]Ide S.Dynamic rupture propagation on a 2D fault with fractal frictional properties[J].Earth Planets&Space,2007,59(10):1099-1109.
[9]Maksimovic'M.New description of the shear strength for rock joints[J].Rock Mechanics&Rock Engineering,1992,25(4):275-284.
[10]Ladanyi B,Archambault G.Simulation of shear behavior of a jointed rock mass[J].US.Symposium on Rock Mechanics,1969,20(11):59-65.
[11]Barton N.Review of a new shear-strength criterion for rock joints[J].Engineering Geology,1973,7(4):287-332.
[12]沈明荣,张清照.规则齿型结构面剪切特性的模型试验研究[J].岩石力学与工程学报,2010,29(4):713-719.Shen Mingrong,Zhang Qingzhao.Experimental study of shear deformation characteristics of rock mass discontinuities[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(4):713-719.
[13]Qi C,Wang M,Bai J,et al.Investigation into size and strain rate effects on the strength of rock-like materials[J].International Journal of Rock Mechanics and Mining Sciences,2016,86:132-140.
[14]张学良,温椒花.基于接触分形理论的结合面切向接触刚度分形模型[J].农业机械学报,2002,33(3):91-93.Zhang Xueliang,Weng Jiaohua.A fractal model of tangential contact stiffness of joint surfaces based on the contact fractal theory[J].Transactions of the Chinese Society of Agricultural Machinery,2002,33(3):91-93.
[15]易成,王长军,张亮,等.基于两体相互作用问题的粗糙表面形貌描述指标系统的研究[J].岩石力学与工程学报,2006,25(12):2481-2492.Yi Cheng,Wang Changjun,Zhang Liang,et al.Study on description index system of rough surface based on bibody interaction[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(12):2481-2492.
[16]Jing L.Numerical modelling of jointed rock masses by Distinct Element Method for two and three-dimensional problems[D].Sweden,Lulea:Lulea University of Technology,1990.
[17]Jing L,Stephansson O,Nordlund E.Study of rock joints under cyclic loading conditions[J].Rock Mechanics&Rock Engineering,1993,26(3):215-232.
[18]Greenwood J A,Williamson J B P.Contact of nominally flat surfaces[J].Proceedings of the Royal Society of London,1966,295(1442):300-319.
[19]Popov V L.接触力学与摩擦学的原理及其应用[M].李强,雒建斌,译.北京:清华大学出版社,2011.
[20]Hamilton G M.Explicit equations for the stresses beneath a sliding spherical contact[J].Archive Proceedings of the Institution of Mechanical Engineers,1983,197(1):53-59.
[21]赵超,钟新谷,刘波,等.基于刚体弹簧法的钢筋混凝土结构破坏过程模拟方法[J].矿业科学学报,2018,3(2):129-138.Zhao Chao,Zhong Xingu,Liu Bo,et al.Numerical simulation of the failure process of reinforced concrete structures based on the rigid body spring method[J].Journal of Mining Science and Technology,2018,3(2):129-138.