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Starting from the thermodynamic framework of a mixture, granular solid hydrodynamics (GSH), which has been developed in recent years, is generalized to the cases in which water and/or gas are present in the interstitials of a granular solid. A preliminary model for the free energy of the mixture is proposed. The three-phase system of grains, water and air is a material relevant to soil mechanics and rock engineering, especially geological catastrophies, for which the macroscopic physics has not been clarified as yet. The engineering theory used currently for analyzing this mixture contains the Darcys law of intersticial flow, the effective stress by Terzaghi, including its equation of motion (i.e., the constitutive relation). Comparing it with the theory of GSH, we clarify that Darcys equation represents mass diffusion, and the effective stress can be explained by the specific model of free energy that is volumetric filling.The usual engineering approach and GSH, a theory based on physics, are consistent, but we do find some discrepancies, especially on how to parameterize the model: the engineering appraoch employs varying constitutive relation, but the physical approach considers the free energy and the transport coefficients. Clarifying this, we believe, is important for eventually obtaining a unified continuous mechanical theory of soils,especially nonsaturated ones, which is complete and satisfying from physicss point of view.
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Keywords:
- granular matter /
- mixture /
- stress /
- hydrodynamics
[1] Yan X, Shi Q, Hou M, Lu K 2003 Phys. Rev. Lett. 91 014302
[2] Fiscina J E, G. Lumay G, Ludewig F, Vandewalle N 2010 Phys. Rev. Lett. 105 048001
[3] Zheng X J, Bo T L 2009 Chin. Sci. Bull. 54 1488 (in Chinese) [郑晓静, 薄天利 2009 科学通报 54 1488]
[4] Royer J R, Corwin E I, Eng P J, Jaeger H M 2007 Phys. Rev. Lett. 99 038003
[5] Lifshitz E M, Landau L D 1987 Fluid Mechanics (New York: Pergamon Press)
[6] Sun Q C, Hou M Y, Jin F 2011 Physics and Mechanics of Granular Matter (Beijing: Science Press) (in Chinese) [孙其诚, 厚美瑛, 金峰 2011 颗粒物质物理与力学(北京: 科学出版社)]
[7] Shen Z J 2000 Theoretical Soil Mechanics (Beijing: China Water Power Press) (in Chinese) [沈珠江 2000 理论土力学(北京: 中国水利水电出版社)]
[8] Martin P C, Parodi O, Pershan P S 1972 Phys. Rev. A 6 2401
[9] Haff P K 1983 J. Fluid Mech. 134 401
[10] Luding S 2009 Nonlinearity 22 R101
[11] Zhao C G, Zhang X D 2008 Sci. China E 38 1453 (in Chinese) [赵成刚, 张雪东 2008 中国科学 E 38 1453]
[12] Jiang Y M, Liu M 2010 Rock and Soil Mechanics 31 1729 (in Chinese) [蒋亦民, 刘佑 2010 岩土力学 31 1729]
[13] Jiang Y M, Liu M 2010 Chin. Sci. Bull. 54 1504 (in Chinese) [蒋亦民, 刘佑 2009 科学通报 54 1504]
[14] Komatsu T S, Inagaki S, Nakagawa N, Nasuno S 2001 Phys. Rev. Lett. 86 1757
[15] Yan X Q, Shi Q F, Hou M Y, Lu K Q 2003 Physics 32 748 (in Chinese) [阎学群, 史庆藩, 厚美瑛, 陆坤权 2003 物理 32 748]
[16] Peng Y J, Liu X S, Zhen Z, Jiang Z H 2011 Physics 40 672 (in Chinese) [彭亚晶, 刘小嵩, 甄珍, 姜泽辉 2011 物理 40 672]
[17] Jiang Z H, Lu K Q, Hou M Y, Chen W, Chen X J 2003 Acta Phys. Sin. 52 2244 (in Chinese) [姜泽辉, 陆坤权, 厚美瑛, 陈唯, 陈相君 2003 52 2244]
[18] Gong X N 2011 Rock and Soil Mechanics 32 321 (in Chinese) [龚晓南 2011 岩土力学 32 321]
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[1] Yan X, Shi Q, Hou M, Lu K 2003 Phys. Rev. Lett. 91 014302
[2] Fiscina J E, G. Lumay G, Ludewig F, Vandewalle N 2010 Phys. Rev. Lett. 105 048001
[3] Zheng X J, Bo T L 2009 Chin. Sci. Bull. 54 1488 (in Chinese) [郑晓静, 薄天利 2009 科学通报 54 1488]
[4] Royer J R, Corwin E I, Eng P J, Jaeger H M 2007 Phys. Rev. Lett. 99 038003
[5] Lifshitz E M, Landau L D 1987 Fluid Mechanics (New York: Pergamon Press)
[6] Sun Q C, Hou M Y, Jin F 2011 Physics and Mechanics of Granular Matter (Beijing: Science Press) (in Chinese) [孙其诚, 厚美瑛, 金峰 2011 颗粒物质物理与力学(北京: 科学出版社)]
[7] Shen Z J 2000 Theoretical Soil Mechanics (Beijing: China Water Power Press) (in Chinese) [沈珠江 2000 理论土力学(北京: 中国水利水电出版社)]
[8] Martin P C, Parodi O, Pershan P S 1972 Phys. Rev. A 6 2401
[9] Haff P K 1983 J. Fluid Mech. 134 401
[10] Luding S 2009 Nonlinearity 22 R101
[11] Zhao C G, Zhang X D 2008 Sci. China E 38 1453 (in Chinese) [赵成刚, 张雪东 2008 中国科学 E 38 1453]
[12] Jiang Y M, Liu M 2010 Rock and Soil Mechanics 31 1729 (in Chinese) [蒋亦民, 刘佑 2010 岩土力学 31 1729]
[13] Jiang Y M, Liu M 2010 Chin. Sci. Bull. 54 1504 (in Chinese) [蒋亦民, 刘佑 2009 科学通报 54 1504]
[14] Komatsu T S, Inagaki S, Nakagawa N, Nasuno S 2001 Phys. Rev. Lett. 86 1757
[15] Yan X Q, Shi Q F, Hou M Y, Lu K Q 2003 Physics 32 748 (in Chinese) [阎学群, 史庆藩, 厚美瑛, 陆坤权 2003 物理 32 748]
[16] Peng Y J, Liu X S, Zhen Z, Jiang Z H 2011 Physics 40 672 (in Chinese) [彭亚晶, 刘小嵩, 甄珍, 姜泽辉 2011 物理 40 672]
[17] Jiang Z H, Lu K Q, Hou M Y, Chen W, Chen X J 2003 Acta Phys. Sin. 52 2244 (in Chinese) [姜泽辉, 陆坤权, 厚美瑛, 陈唯, 陈相君 2003 52 2244]
[18] Gong X N 2011 Rock and Soil Mechanics 32 321 (in Chinese) [龚晓南 2011 岩土力学 32 321]
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