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The mixture of scrap rubber particles and sands has been extensively used as geotechnical engineering recycled materials due to its environmental protection performance, light quality and excellent energy dissipation capability. The mechanical properties of the system can be modulated by the mixing ratio between soft and hard components. But the reasons for such a change on a particle scale are not yet clear. In this paper the elastic behaviors of glass-rubber mixed particles are studied by the sound velocity measurement and discrete element simulation. The velocity of compressional wave and the dynamic effective elastic modulus of mixed sample under hydrostatic stress are measured by time-of-flight method. It is found that the wave velocity is almost constant and the modulus decreases slightly with the proportion of rubber particles increasing to 20%. After that the wave velocity and modulus decrease rapidly and the system transforms from rigid-like behavior to soft-like behavior until the proportion of rubber particles reaches to 80%. When the proportion of rubber particles are more than 80%, the compressional wave velocity and the dynamic effective elastic modulus remain stable again. Such experimental results are consistent with discrete element method analyses which provide more in-depth insights into the micromechanics of the mixture. The simulation reveals that at low rubber fraction the main force chain structure is basically composed of glass particles without rubber particles, which accounts for the phenomenon that the velocity of the compressional wave is basically constant. When the glass particles and rubber particles co-construct the main force chain structure, the distribution of the normal contact force is relatively uniform at high rubber fraction. This can be regarded as the glass particles suspending in the rubber particles. An improved effective medium theory is proposed to describe the elastic behavior of the mixed particles system. It is considered that the deformation of the internal particles is relatively uniform for glass dominated mixture which satisfies the isostress hypothesis. A parallel spring model can be used to describe the nonlinear contact model of particles in such materials. On the other hand, rubber dominated mixture approximately satisfies the isostrain hypothesis, which can be described by a series spring model. The outcomes of such models are in agreement with the simulation results for rigid glass dominated mixture and soft rubber dominated mixture. This study is helpful in exploring the mechanisms that are responsible for the macroscale elastic behavior of mixed granular material from the microscopic point of view.
[1] Jaeger H M, Nagel S R, Behringer R P 1996 Rev. Mod. Phys. 68 1259
[2] Liu C Q, Sun Q C, Wang G Q 2014 Mech. Engineer. 36 716 (in Chinese)[刘传奇, 孙其诚, 王光谦 2014 力学与实践 36 716]
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[7] Li L H, Xiao H L, Tang H M, Hu Q Z, Sun M J, Sun L 2014 Rock and Soil Mechanics 35 359 (in Chinese)[李丽华, 肖衡林, 唐辉明, 胡其志, 孙淼军, 孙龙 2014 岩土力学 35 359]
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[9] Chen Q, Wang Q H, Zhao C, Zhang Q, Hou M Y 2015 Acta Phys. Sin. 64 154502 (in Chinese)[陈琼, 王青花, 赵闯, 张祺, 厚美瑛 2015 64 154502]
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[13] Zhang P, Zhao X D, Zhang G H, Zhang Q, Sun Q C, Hou Z J, Dong J J 2016 Acta Phys. Sin. 65 024501 (in Chinese)[张攀, 赵雪丹, 张国华, 张祺, 孙其诚, 侯志坚, 董军军 2016 65 024501]
[14] Zheng H P, Jiang Y M, Peng Z, Fu L P 2012 Acta Phys. Sin. 61 214502 (in Chinese)[郑鹤鹏, 蒋亦民, 彭政, 符力平 2012 61 214502]
[15] Zhang Q, Li Y, Hou M, Jiang Y, Liu M 2012 Phys. Rev. E 85 031306
[16] Zhou Z G, Zong J, Wang W G, Hou M Y 2017 Acta Phys. Sin. 66 154502 (in Chinese)[周志刚, 宗谨, 王文广, 厚美瑛 2017 66 154502]
[17] Khidas Y, Jia X P 2012 Phys. Rev. E:Stat. Nonlin. Soft Matter Phys. 85 051302
[18] Liu X Y, Jiao T F, Ma L, Su J Y, Chen W Z, Sun Q C, Huang D C 2017 Granular Matter 19 55
[19] Taghizadeh K, Steeb H, Magnanimo V, Luding S 2017 Powders & Grains Montpellier, France, July 3-7 2017 p12019
[20] Qian Z W 2012 Acta Phys. Sin. 61 134301 (in Chinese)[钱祖文 2012 61 134301]
[21] Di Renzo A, Di Maio F P 2004 Chem. Engineer. Sci. 59 525
[22] Han Y L, Jia F G, Tang Y R, Liu Y, Zhang Q 2014 Acta Phys. Sin. 63 174501 (in Chinese)[韩燕龙, 贾富国, 唐玉荣, 刘扬, 张强 2014 63 174501]
[23] Chen H, Liu Y L, Zhao X Q, Xiao Y G, Liu Y 2015 Powder Technol. 283 607
[24] Snoeijer J H, Vlugt T J, van Hecke M, van Saarloos W 2004 Phys. Rev. Lett. 92 054302
[25] Hashin Z, Shtrikman S 1963 J. Mech. Phys. Solids 11 127
[26] Yang X S, Ma J, Liu L Q 2004 Seismol. Geol. 26 484 (in Chinese)[杨晓松, 马瑾, 刘力强 2004 地震地质 26 484]
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[1] Jaeger H M, Nagel S R, Behringer R P 1996 Rev. Mod. Phys. 68 1259
[2] Liu C Q, Sun Q C, Wang G Q 2014 Mech. Engineer. 36 716 (in Chinese)[刘传奇, 孙其诚, 王光谦 2014 力学与实践 36 716]
[3] Kou B Q, Cao Y X, Li J D, Xia C J, Li Z F, Dong H P, Zhang A, Zhang J, Kob W, Wang Y J 2017 Nature 551 360
[4] Wang S M, Gao Y F 2007 Rock and Soil Mechanics 28 1001 (in Chinese)[王庶懋, 高玉峰 2007 岩土力学 28 1001]
[5] Chen Y N, Xiao J M 2015 Chin. J. Engineer. 37 1498 (in Chinese)[陈亚楠, 肖久梅 2015 工程科学学报 37 1498]
[6] Liu W X, Wu P W, Dai J H 2017 Develop. Appl. Mater. 32 27 (in Chinese)[柳文鑫, 吴平伟, 戴金辉 2017 材料开发与应用 32 27]
[7] Li L H, Xiao H L, Tang H M, Hu Q Z, Sun M J, Sun L 2014 Rock and Soil Mechanics 35 359 (in Chinese)[李丽华, 肖衡林, 唐辉明, 胡其志, 孙淼军, 孙龙 2014 岩土力学 35 359]
[8] Lee J S, Dodds J, Santamarina J C 2007 J. Mater. Civil Engineer. 19 179
[9] Chen Q, Wang Q H, Zhao C, Zhang Q, Hou M Y 2015 Acta Phys. Sin. 64 154502 (in Chinese)[陈琼, 王青花, 赵闯, 张祺, 厚美瑛 2015 64 154502]
[10] Qian Z W 1993 Appl. Acoust. 12 1 (in Chinese)[钱祖文 1993 应用声学 12 1]
[11] Jia X P, Caroli C, Velicky B 1999 Phys. Rev. Lett. 82 1863
[12] Jia X P 2004 Phys. Rev. Lett. 93 154303
[13] Zhang P, Zhao X D, Zhang G H, Zhang Q, Sun Q C, Hou Z J, Dong J J 2016 Acta Phys. Sin. 65 024501 (in Chinese)[张攀, 赵雪丹, 张国华, 张祺, 孙其诚, 侯志坚, 董军军 2016 65 024501]
[14] Zheng H P, Jiang Y M, Peng Z, Fu L P 2012 Acta Phys. Sin. 61 214502 (in Chinese)[郑鹤鹏, 蒋亦民, 彭政, 符力平 2012 61 214502]
[15] Zhang Q, Li Y, Hou M, Jiang Y, Liu M 2012 Phys. Rev. E 85 031306
[16] Zhou Z G, Zong J, Wang W G, Hou M Y 2017 Acta Phys. Sin. 66 154502 (in Chinese)[周志刚, 宗谨, 王文广, 厚美瑛 2017 66 154502]
[17] Khidas Y, Jia X P 2012 Phys. Rev. E:Stat. Nonlin. Soft Matter Phys. 85 051302
[18] Liu X Y, Jiao T F, Ma L, Su J Y, Chen W Z, Sun Q C, Huang D C 2017 Granular Matter 19 55
[19] Taghizadeh K, Steeb H, Magnanimo V, Luding S 2017 Powders & Grains Montpellier, France, July 3-7 2017 p12019
[20] Qian Z W 2012 Acta Phys. Sin. 61 134301 (in Chinese)[钱祖文 2012 61 134301]
[21] Di Renzo A, Di Maio F P 2004 Chem. Engineer. Sci. 59 525
[22] Han Y L, Jia F G, Tang Y R, Liu Y, Zhang Q 2014 Acta Phys. Sin. 63 174501 (in Chinese)[韩燕龙, 贾富国, 唐玉荣, 刘扬, 张强 2014 63 174501]
[23] Chen H, Liu Y L, Zhao X Q, Xiao Y G, Liu Y 2015 Powder Technol. 283 607
[24] Snoeijer J H, Vlugt T J, van Hecke M, van Saarloos W 2004 Phys. Rev. Lett. 92 054302
[25] Hashin Z, Shtrikman S 1963 J. Mech. Phys. Solids 11 127
[26] Yang X S, Ma J, Liu L Q 2004 Seismol. Geol. 26 484 (in Chinese)[杨晓松, 马瑾, 刘力强 2004 地震地质 26 484]
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