光弹颗粒材料直剪实验研究
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摘要
众多学者认为,进一步促进岩土力学发展和变革的关键在于,从颗粒尺度来重新认识这门学科。众多的研究均表明,颗粒材料中平均强度力链和几何结构对材料宏观的力学和变形性质均起着重要的作用。本文借助光弹实验手段和数字图像处理方法,通过研制的直剪仪,初步探讨了颗粒材料在直剪作用下,颗粒几何结构和平均强度力链分布之间的关系。
本文设计研制了直剪仪,并进行了光弹材料的制备和退火等前期准备工作,得到了本实验光弹颗粒的退火曲线。通过引入的平均彩色梯度的算法,实验拟合得到了,颗粒的平均接触力F和平均彩色梯度的关系曲线,该关系曲线是颗粒材料中平均强度力链识别的重要力学基础。
本文对光弹实验拍摄得到的数码图像进行处理,识别得到了颗粒材料的几何位置信息,在此基础上,结合彩色梯度算法获取得到的光弹颗粒材料力学信息,最终识别得到颗粒材料中的接触向量角度分布图和平均强度力链分布图。
基于数字图像处理获得的结果,建立平均配位数和剪切变形的关系,解释了直剪过程中的剪胀和剪缩现象;对直剪作用下的接触向量角度分布进行统计分析,并定义了“极化角区间”等概念,结果表明:初始阶段,颗粒材料的几何结构基本上呈现各向异性。在直剪过程中,随着剪应力的增大,其各向异性越来越明显,当达到峰值强度时,其各向异性最为明显。颗粒材料初始状态固有的各向异性对加载过程中几何结构的各向异性有较大的影响。同时,颗粒材料直剪过程中的接触向量角度分布,受到颗粒材料的初始状态固有的各向异性影响。本文还对接触向量初始极化角和平均强度力链分布进行分析,结果表明:当颗粒材料施加剪应力后,剪切力的逐渐增大诱发了几何结构的各向异性,出现了极化角区间,而几何结构的各向异性则导致了平均强度力链在这些极化角度区间内大量分布,从而引起平均强度力链分布的局部化。
本文仅对平均强度力链和几何结构的关系进行初步的探讨,更加深入的研究仍在继续。
It is agreed among many researchers that the approach of granular geo-mechanics is the key to the better understanding of fundamentals of geo-materials. The force chain and fabric of photo-elastic granular assemblies as crucial to the phenomenological properties of geo-materials were studied in a direct shear box in the present thesis using photo-elastic and digital image analysis techniques.
First, a direct shear box filled with the photo-elastic bi-disperse discs was made transparent to the polarized light. The residual stress of discs due to manufacturing was removed with the specified anneal treatment preceding the tests. The so-called average color gradient of each disc was calculated to analyze the force information captured in the photo-elastic images during the direct shearing followed with the obtained correlation of with the average contact force of each disc.
In parallel, the digital image analysis was also performed to extract the kinetic information of each disc during the direct shearing. The kinetic and force information extracted from the sequence of photos enabled the quantitative description of contact network and force chain developed in the granular assembly due to slow direct shearing.
The well known phenomenon of dilatancy and compression were eventually impetrated as the variance of the average coordination number of whole granular assembly. The statistics of the inclinations of branching vectors revealed the strong inherent anisotropy which even enhanced in the following shearing. The anisotropy becomes more and more obvious as the increasing of the shear strength. Having analyzed both the characteristics of contact vector and force chain induced suggested that the anisotropy of contact vector induced by the increasing shear force results in the localization of the force chains.
本文设计研制了直剪仪,并进行了光弹材料的制备和退火等前期准备工作,得到了本实验光弹颗粒的退火曲线。通过引入的平均彩色梯度的算法,实验拟合得到了,颗粒的平均接触力F和平均彩色梯度
本文对光弹实验拍摄得到的数码图像进行处理,识别得到了颗粒材料的几何位置信息,在此基础上,结合彩色梯度算法获取得到的光弹颗粒材料力学信息,最终识别得到颗粒材料中的接触向量角度分布图和平均强度力链分布图。
基于数字图像处理获得的结果,建立平均配位数和剪切变形的关系,解释了直剪过程中的剪胀和剪缩现象;对直剪作用下的接触向量角度分布进行统计分析,并定义了“极化角区间”等概念,结果表明:初始阶段,颗粒材料的几何结构基本上呈现各向异性。在直剪过程中,随着剪应力的增大,其各向异性越来越明显,当达到峰值强度时,其各向异性最为明显。颗粒材料初始状态固有的各向异性对加载过程中几何结构的各向异性有较大的影响。同时,颗粒材料直剪过程中的接触向量角度分布,受到颗粒材料的初始状态固有的各向异性影响。本文还对接触向量初始极化角和平均强度力链分布进行分析,结果表明:当颗粒材料施加剪应力后,剪切力的逐渐增大诱发了几何结构的各向异性,出现了极化角区间,而几何结构的各向异性则导致了平均强度力链在这些极化角度区间内大量分布,从而引起平均强度力链分布的局部化。
本文仅对平均强度力链和几何结构的关系进行初步的探讨,更加深入的研究仍在继续。
It is agreed among many researchers that the approach of granular geo-mechanics is the key to the better understanding of fundamentals of geo-materials. The force chain and fabric of photo-elastic granular assemblies as crucial to the phenomenological properties of geo-materials were studied in a direct shear box in the present thesis using photo-elastic and digital image analysis techniques.
First, a direct shear box filled with the photo-elastic bi-disperse discs was made transparent to the polarized light. The residual stress of discs due to manufacturing was removed with the specified anneal treatment preceding the tests. The so-called average color gradient
In parallel, the digital image analysis was also performed to extract the kinetic information of each disc during the direct shearing. The kinetic and force information extracted from the sequence of photos enabled the quantitative description of contact network and force chain developed in the granular assembly due to slow direct shearing.
The well known phenomenon of dilatancy and compression were eventually impetrated as the variance of the average coordination number of whole granular assembly. The statistics of the inclinations of branching vectors revealed the strong inherent anisotropy which even enhanced in the following shearing. The anisotropy becomes more and more obvious as the increasing of the shear strength. Having analyzed both the characteristics of contact vector and force chain induced suggested that the anisotropy of contact vector induced by the increasing shear force results in the localization of the force chains.
引文
[1]贾鲁强.漫谈颗粒物理.物理双月刊,2001,23(4):1-9
[2] Hartley R Ryan. Evolving force networks in deforming granular material: [Doctoral dissertation]. Duke University, USA: 2003
[3] Santamarina J Carlos, Soil Behavior at the Micro-scale: Particle Forces. Proc Symp Soil Behavior and Soft Ground Construction-in honor of Charles C. Ladd at MIT, 2001:1-32
[4] Terzaghi K, Old Earth Pressure Theories and New Test Results. Engineering News-Record, 1920, 85(14): 632-637
[5] Dantu P. A Contribution to the Mechanical and Geometrical Study of Non-conhesive Masses. Proc. Int. Conf. Soil. Mech& Found. Eng, London, Vol.1: 144-148
[6] De Josselin de Jong G, Verruijt A. Etude photo-elastique d'un empilement de disques. Cahiers du group Francais de Rheologie, Janvier 1969, vol. II: 73–86
[7] Cundall P A, Strack O.D.L. A discrete numerical model for granular assemblies. Géotechnique, 1979, 29(1): 47-65
[8] Drescher A, De Josselin de Jong G. Photoelastic verification of a mechanical model for the flow of a granular material. J. Mech. Phy. Solids, 1972, 20: 337–351
[9] Geng Junfei. Green’s function measurement of force transmission in 2D granular material. Physica D, 2003, 182: 274-303
[10] Peters J F, Muthuswamy M and Wibowo J, et al. Characterization of force chains in granular material. Physical review E, 2005, 72:1-7
[11] Jacco H Snoeijer, Thijs J H Vlugt, Martin van Hecke, et. al. Force Network Ensemble: A New Approach to Static Granular Matter. Physical Review Letters, 2004, 92(5): 054302-1-4
[12] Bosko J T, Tordesillas A. Evolution of Contact Forces, Fabric, and their Collective Behavior in Granular Media under Deformation: A DEM Study. Earth and Space 2006 Proceedings of the 10th ASCE Aerospace Division of International Conference on Engineering, Construction and Operations in Challenging Environments, 2006: 1-8
[13] Goldenberg C, Goldhirsch I. Force chains, microelasticity, and macroelasticity. Physical Review Letters, 2002, 89(3): 0804302-1-4
[14]刘斯宏,徐永福.粒状体直剪试验的数值模拟与微观考察.岩石力学与工程学报,2001,20(3):288～292
[15] WU Aixiang, YANG Baohua. Fractal analysis of granular ore media based on computedtomography image processing. Trans. Nonferrous Met. Soc. China 2008,18:1523-1528
[16] Lueptow R M, Akonur. PIV for granular flows. Experiments in Fluids, 2000, 28(2):183-186
[17] Olivier Tsoungui, Denis Vallet, Jean-Claude Charmet. Use of contact area trace to study the force distributions inside 2D granular systems. Granular Matter, 1998, 1: 65-69
[18] Lovoll G, Maloy K J, Flekkoy E G. Force measurements on static granular materials. Physical Review E, 1999, 60: 5872-5878
[19] Frocht M. M. Photoelasticity (I). New York: John Wiley&Sons, Inc., 1941
[20] Neumann F. E. Berichte Koniff. Preuss. Akad, Wssensch. 1840, Abh. der Konigl. Akad.der Wissensch. Berlin Part B, 50, 1841.
[21] Maxwell J. C. Traps. R Soc. Edinburgh, 1853: 20:87
[22] N. P. Kruyt, S. J. Antony. Force, relative-displacement, and work networks in granular materials subjected to quasistatic deformation. Physical review E, 2007,75(5): 1-8
[23] Thornton C. Numerical simulations of deviatoric shear deformation of granular media. Geotechnique, 2000, 50(4): 43-53
[24] M.Oda, J.Konishi. Some experimentally based fundamental results on the mechanical behavior of granular material: Effects of particle rolling, Géotechnique, 1980, 30(4): 479-495
[25] Oda M, Konishi J, Nemat-Nasser S. Experimental micro-mechanical evaluation of strength of granular materials: effect of particle rolling. Mechanic. Materials 1, 1982, 269-283
[26] Drescher, A. An experimental investigation of flow rules for granular materials using optically sensitive glass particles, Géotechnique , 1976, 26(4): 591-901
[27] Allersma, H.G.B. Optical Analysis of stress and strain in photoelastic particle assemblies: [Doctoral dissertation]. TU-Delft, Netherlands: 1987
[28] Allersma, H.G.B. Optical Analysis of Stress and Strain Around Penetrating Elements in a Granular Medium. Int. Conference on Offshore and Polar Engineering, 2005, seoul: 590-596
[29] Shukla A, Nigam H. Experimental investigation of wave velocityand dynamic contact stresses in an assembly of disks. J. of Strain Analysis, 1985, 20(2):121-129
[30] Baxter G.W. Stress distributions in a two dimensional granular material. In R.P. Behringer and J.T. Jenkins, editors, Powders and Grains97, 1997:345-348
[31] Howell Daniel Wyatt. Stress distribution and fluctuations in static and quasi-static granular systems: [Doctoral dissertation]. Duke University, USA: 1999
[32] Fluctuations in granular media. Daniel W. Howell , R. P. Behringe. Chaos, 1999, 9(3):559-572
[33] Junfei Geng, D. Howell, E. Longhi. Footprints in Sand: The Response of a Granular Material to Local Perturbations. Physical review letters, 2001, 87(3):1-4
[34] Hartley R R, Behringer R P. Logarithmic rate dependence of force networks in sheared granular materials. Nature, 2003, 421(27): 928-931
[35] Behringer R P, Howell Daniel Wyatt, Kondic Lou, et al. Predictability and granular materials. Physica D, 1999, 133: 1–17
[36] Majmudar T S, Sperl M, LudingJamming S, et al. Jamming Transition in Granular Systems. Physical Review Letters, 2007, 98(2): 058001-1-4
[37] Majmudar T S, Behringer R P. Contact force measurements and stress-induced anisotropy in granular materials. Nature,2005, 435(2): 1079-1082
[38] Majmudar T S. Experimental studies of two-dimensional granular material systems using grain-scale contact forces measurements: [Doctoral dissertation]. Duke University, USA: 2006
[39]天津大学材料力学组.光弹性原理及测试技术.北京:科学出版社, 1980
[40]贺幼良,白润光,宋宝韫.三维高温光塑性及其应用.锻压机械.1998, 3: 45-47
[41]铁摩辛柯,古地尔著,徐芝纶译.弹性理论.北京:高等教育出版社,1990. 75-166
[42] Rafael C Gonzalez,阮秋奇等译.数字图像处理,.北京:电子工业出版社, 2006
[43] Calvetti1 F, Combe G., Experimental micromechanical analysis of a 2D granular material:relation between structure evolution and loading path. Mechanics of cohersive frictional material, 1997, 2(2): 121–163
[44] Blumenfeld Raphael. Stresses in isostatic granular systems and emergence of force chains. Physical Review Letters, 2004, 93(10): 108301-1-4
[2] Hartley R Ryan. Evolving force networks in deforming granular material: [Doctoral dissertation]. Duke University, USA: 2003
[3] Santamarina J Carlos, Soil Behavior at the Micro-scale: Particle Forces. Proc Symp Soil Behavior and Soft Ground Construction-in honor of Charles C. Ladd at MIT, 2001:1-32
[4] Terzaghi K, Old Earth Pressure Theories and New Test Results. Engineering News-Record, 1920, 85(14): 632-637
[5] Dantu P. A Contribution to the Mechanical and Geometrical Study of Non-conhesive Masses. Proc. Int. Conf. Soil. Mech& Found. Eng, London, Vol.1: 144-148
[6] De Josselin de Jong G, Verruijt A. Etude photo-elastique d'un empilement de disques. Cahiers du group Francais de Rheologie, Janvier 1969, vol. II: 73–86
[7] Cundall P A, Strack O.D.L. A discrete numerical model for granular assemblies. Géotechnique, 1979, 29(1): 47-65
[8] Drescher A, De Josselin de Jong G. Photoelastic verification of a mechanical model for the flow of a granular material. J. Mech. Phy. Solids, 1972, 20: 337–351
[9] Geng Junfei. Green’s function measurement of force transmission in 2D granular material. Physica D, 2003, 182: 274-303
[10] Peters J F, Muthuswamy M and Wibowo J, et al. Characterization of force chains in granular material. Physical review E, 2005, 72:1-7
[11] Jacco H Snoeijer, Thijs J H Vlugt, Martin van Hecke, et. al. Force Network Ensemble: A New Approach to Static Granular Matter. Physical Review Letters, 2004, 92(5): 054302-1-4
[12] Bosko J T, Tordesillas A. Evolution of Contact Forces, Fabric, and their Collective Behavior in Granular Media under Deformation: A DEM Study. Earth and Space 2006 Proceedings of the 10th ASCE Aerospace Division of International Conference on Engineering, Construction and Operations in Challenging Environments, 2006: 1-8
[13] Goldenberg C, Goldhirsch I. Force chains, microelasticity, and macroelasticity. Physical Review Letters, 2002, 89(3): 0804302-1-4
[14]刘斯宏,徐永福.粒状体直剪试验的数值模拟与微观考察.岩石力学与工程学报,2001,20(3):288～292
[15] WU Aixiang, YANG Baohua. Fractal analysis of granular ore media based on computedtomography image processing. Trans. Nonferrous Met. Soc. China 2008,18:1523-1528
[16] Lueptow R M, Akonur. PIV for granular flows. Experiments in Fluids, 2000, 28(2):183-186
[17] Olivier Tsoungui, Denis Vallet, Jean-Claude Charmet. Use of contact area trace to study the force distributions inside 2D granular systems. Granular Matter, 1998, 1: 65-69
[18] Lovoll G, Maloy K J, Flekkoy E G. Force measurements on static granular materials. Physical Review E, 1999, 60: 5872-5878
[19] Frocht M. M. Photoelasticity (I). New York: John Wiley&Sons, Inc., 1941
[20] Neumann F. E. Berichte Koniff. Preuss. Akad, Wssensch. 1840, Abh. der Konigl. Akad.der Wissensch. Berlin Part B, 50, 1841.
[21] Maxwell J. C. Traps. R Soc. Edinburgh, 1853: 20:87
[22] N. P. Kruyt, S. J. Antony. Force, relative-displacement, and work networks in granular materials subjected to quasistatic deformation. Physical review E, 2007,75(5): 1-8
[23] Thornton C. Numerical simulations of deviatoric shear deformation of granular media. Geotechnique, 2000, 50(4): 43-53
[24] M.Oda, J.Konishi. Some experimentally based fundamental results on the mechanical behavior of granular material: Effects of particle rolling, Géotechnique, 1980, 30(4): 479-495
[25] Oda M, Konishi J, Nemat-Nasser S. Experimental micro-mechanical evaluation of strength of granular materials: effect of particle rolling. Mechanic. Materials 1, 1982, 269-283
[26] Drescher, A. An experimental investigation of flow rules for granular materials using optically sensitive glass particles, Géotechnique , 1976, 26(4): 591-901
[27] Allersma, H.G.B. Optical Analysis of stress and strain in photoelastic particle assemblies: [Doctoral dissertation]. TU-Delft, Netherlands: 1987
[28] Allersma, H.G.B. Optical Analysis of Stress and Strain Around Penetrating Elements in a Granular Medium. Int. Conference on Offshore and Polar Engineering, 2005, seoul: 590-596
[29] Shukla A, Nigam H. Experimental investigation of wave velocityand dynamic contact stresses in an assembly of disks. J. of Strain Analysis, 1985, 20(2):121-129
[30] Baxter G.W. Stress distributions in a two dimensional granular material. In R.P. Behringer and J.T. Jenkins, editors, Powders and Grains97, 1997:345-348
[31] Howell Daniel Wyatt. Stress distribution and fluctuations in static and quasi-static granular systems: [Doctoral dissertation]. Duke University, USA: 1999
[32] Fluctuations in granular media. Daniel W. Howell , R. P. Behringe. Chaos, 1999, 9(3):559-572
[33] Junfei Geng, D. Howell, E. Longhi. Footprints in Sand: The Response of a Granular Material to Local Perturbations. Physical review letters, 2001, 87(3):1-4
[34] Hartley R R, Behringer R P. Logarithmic rate dependence of force networks in sheared granular materials. Nature, 2003, 421(27): 928-931
[35] Behringer R P, Howell Daniel Wyatt, Kondic Lou, et al. Predictability and granular materials. Physica D, 1999, 133: 1–17
[36] Majmudar T S, Sperl M, LudingJamming S, et al. Jamming Transition in Granular Systems. Physical Review Letters, 2007, 98(2): 058001-1-4
[37] Majmudar T S, Behringer R P. Contact force measurements and stress-induced anisotropy in granular materials. Nature,2005, 435(2): 1079-1082
[38] Majmudar T S. Experimental studies of two-dimensional granular material systems using grain-scale contact forces measurements: [Doctoral dissertation]. Duke University, USA: 2006
[39]天津大学材料力学组.光弹性原理及测试技术.北京:科学出版社, 1980
[40]贺幼良,白润光,宋宝韫.三维高温光塑性及其应用.锻压机械.1998, 3: 45-47
[41]铁摩辛柯,古地尔著,徐芝纶译.弹性理论.北京:高等教育出版社,1990. 75-166
[42] Rafael C Gonzalez,阮秋奇等译.数字图像处理,.北京:电子工业出版社, 2006
[43] Calvetti1 F, Combe G., Experimental micromechanical analysis of a 2D granular material:relation between structure evolution and loading path. Mechanics of cohersive frictional material, 1997, 2(2): 121–163
[44] Blumenfeld Raphael. Stresses in isostatic granular systems and emergence of force chains. Physical Review Letters, 2004, 93(10): 108301-1-4