GUAN Cheng-yao, QI Jia-fu, QIU Nan-sheng, ZHAO Guo-chun, LI Chun-lei, YANG Qiao, BAI Xiang-dong. Three Levels Friction Coefficient of Cracks and Its Influencing Factors—Taking the Sandstone (Particle Packing Layers) as an Example[J]. Applied Mathematics and Mechanics, 2013, 34(2): 209-216. doi: 10.3879/j.issn.1000-0887.2013.02.011
 Citation: GUAN Cheng-yao, QI Jia-fu, QIU Nan-sheng, ZHAO Guo-chun, LI Chun-lei, YANG Qiao, BAI Xiang-dong. Three Levels Friction Coefficient of Cracks and Its Influencing Factors—Taking the Sandstone (Particle Packing Layers) as an Example[J]. Applied Mathematics and Mechanics, 2013, 34(2): 209-216.

# Three Levels Friction Coefficient of Cracks and Its Influencing Factors—Taking the Sandstone (Particle Packing Layers) as an Example

##### doi: 10.3879/j.issn.1000-0887.2013.02.011
• Rev Recd Date: 2013-01-10
• Publish Date: 2013-02-15
• To build a friction factors model of friction surface and dividing the friction factors into three levels, there were respectively the friction coefficient of surfaces of sand particles, average friction coefficient of asperities inclined plane, rocks surfaces (or macroscopic crack). The coupling of three levels the friction factors was the key determinants of the practical friction coefficient. The friction coefficient of rocks was from the friction factors of surfaces of sand particles and was amplified by the later two levels. And the selfsimilar series asperities themselves can amplify friction coefficients many times. The average angle of asperities inclined plane or fractal dimension is the key influencing factors and the key reason of the differentiation. The influencing factors of arrangements of particles are smaller relatively. The static friction coefficient is bigger than coefficient of the sliding friction caused by the average contact angle.
•  [1] 孙其诚, 厚美瑛, 金峰.颗粒物质物理与力学[M].北京：科学出版社, 2011:191-193.(SUN Qi-cheng, HOU Mei-ying, JIN Feng. The Physical and Mechanical of Granular Materials [M].Beijing: Science Press, 2011:191-193.(in Chinese)) [2] 安欧.构造应力场[M].北京: 地震出版社.1992: 133134.(AN-OU. Tectonic Stress Field [M].Beijing: Earthquake Publishing House, 1992: 133-134.(in Chinese)) [3] 温诗铸, 黄平.摩擦学原理[M].第二版.北京：清华大学出版社.2002.256-270.(WEN Shi-zhu, HUANG Ping. Tribology Principle [M].2nd ed.Beijing: Tsinghua University Publishing House, 2002: 256-270.(in Chinese)) [4] Halling J. Principles of Tribology [M].New York: Mcmillan Press Ltd.1975: 1-401. [5] 瓦伦丁L.波波夫.接触力学与摩擦学的原理与应用[M].李强, 雒建斌 译.北京：清华大学出版社, 2011: 1-284.(Valentin L.Popov. Contact Mechanics and Friction Physical Principles and Applications [M].Beijing: Tsinghua University Publishing House, 2011: 1-284.(Chinese version)) [6] 孙其诚, 王光谦.颗粒物质力学导论[M].北京：科学出版社, 2010.(SUN Qi-cheng, WANG Guang-qian. Introduction to the Physical and Mechanical of Granular Materials [M].Beijing: Science Press, 2010.(in Chinese)) [7] Johnson K L. Contact Mechanics [M].Cambridge: Cambridge University Press, 1985: 207-209. [8] Oda M, Iwashita K. Mechanics of Granular Materials, an Introduction [M].Oxford: Taylor & Francis Group, 1999: 207-209. [9] Greenwood J A, Williamson J B.Contact of nominally flat surface[J]. Proc Roy Soc A,1966, 295 (3): 300-319. [10] GUAN Chengyao, QI Jiafu, QIU Nansheng.Macroscopic Young’s elastic modulus model of particle packing rock layers[J]. Open Journal of Geology, 2012, 2(3): 198-202. [11] 曾凡, 胡永平.矿物加工颗粒学[M].徐州:中国矿业大学出版社,2001: 92-93.（ZENG Fan, HU Yong-ping. Particle Technology of Mineral Processing [M].Xuzhou: China University of Mining Press, 2001: 92-93.(in Chinese)） [12] O’Sullivan C, Bray J D, Riemer M.Examination of the response of regularly packed specimens of spherical partical particles using physical tests and discrete element simulations[J]. J Eng Mech,2004, 130(1):1140-1150. [13] 谢和平, 陈忠辉.岩石力学[M].北京：科学出版社, 2004: 230-257.(XIE He-ping, CHEN Zhong-hui. Rock Mechanics [M].Beijing: Science Press, 2004: 230-257.(in Chinese)) [14] Prandtl L.Ein Gedankenmodell zur kinetischen Theorie der festen Korper[J]. ZAMM,1928, 8(2): 85-106. [15] Tomlinson G A.A molecular theory of friction[J]. Science,1929,7(46 supplement): 905-939.(The London, Edinburgh, and Dublin Philosphical Magazine) .Oxford:Taylor & Francis Group) [16] Hartmut Hetzler.On moving continua with contacts and sliding friction: modeling, general properties and examples[J]. International Journal of Solids and Structures,2009, 46(4):2556-2570. [17] Adams G G, Nosonovsky M.Contact modelingforces[J]. Tribology International, 2000, 192(33): 431-442. [18] Tabor D.Friction—the present state of our understanding[J].ASME J Lubrication Tech,1981,93(103):169-179. [19] Bengisu M T, Akay A.Relation of dryfriction to surface roughness[M]. ASME J Tribol,1997, 119 (13):18-25. [20] Oden J T, Martins J A C .Models and computational methods for dynamic friction phenomena[J].Com Meth Appl Mech Engng,1985, 56(15):527-634. [21] Martins J A C, Oden J T, Simes F M F.A study of static and kinetic friction[J]. Int J Engng Sci,1990, 123(28):29-92. [22] Martins J A C, Guimares J, Faria L O.Dynamic surface solutions in linear elasticity and viscoelaticity with frictional boundary conditions[J]. ASME J Vib Acou,1995, 117(92): 445-451. [23] Adams G G.Selfexcited oscillations in sliding with a constant friction coefficient—a simple model[J]. ASME J Tribol,1996, 118(31):819-823. [24] 关成尧, 漆家福, 邱楠生.应力比影响下的压剪裂纹破裂角、闭锁角、摩擦因数及其耦合关系[J].岩土力学, 2012, 33(12):3570-3576.(GUAN Cheng-yao, QI Jia-fu, QIU Nan-sheng.Crack angle,lock angle,friction coefficient under stress ratio affected and its coupling relationship in a compressionshear crack[J]. Rock and Soil Mechanics,2012, 33(12):3570-3576.(in Chinese))

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