Hydrodynamic theory of grains, water and air

Jiang Yi-Min; Liu Mario

doi:10.7498/aps.62.204501

Abstract

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.

Keywords:

PACS:

43.20.+g	(General linear acoustics)
43.40.+s	(Structural acoustics and vibration)
43.55.+p	(Architectural acoustics)

Authors and contacts

Jiang Yi-Min¹,
Liu Mario²

1.
School of Physics and Electronics, Central South University, Changsha 410083, China;
2.
Theoretische Physik, Universität Tübingen, Tübingen 72076, Germany
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11274390).

References

[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 物理学报 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]

Cited By

期刊类型引用(12)

1.	辛雨柯，邓庆田，宋学力，李新波. 加筋曲板结构抗弯承载能力分析. 塑性工程学报. 2024(02): 189-198 . 百度学术
2.	毛军喜，欧立新，孔德睿，陈韬，张迅. 钢混加强圈对钢波纹板裸拱涵动力特性的影响研究. 施工技术(中英文). 2024(18): 32-37 . 百度学术
3.	汤冬，马梓铜，张克澳，王汝鹏，辛松刚. 正交加筋板中板梁耦合动力特性. 中国舰船研究. 2023(04): 265-275 . 百度学术
4.	马天兵，丁威海，周青，杜菲. 基于改进滑模变结构的加筋板振动控制研究. 安徽理工大学学报(自然科学版). 2021(01): 7-12 . 百度学术
5.	孔德睿，张迅，刘子琦，游颖川，郑宁哲，周靖翔. 基于颗粒阻尼的U肋加劲板减振降噪初探. 噪声与振动控制. 2021(05): 38-44 . 百度学术
6.	周海安，修孝廷，孟建兵. 基于有限元/边界元的双层周期加筋板声辐射分析. 山东理工大学学报(自然科学版). 2019(03): 31-36+42 . 百度学术
7.	ZHOU Haian，WANG Xiaoming，WU Huayong，MENG Jianbing，LI Lijun. Efficient semi-analytical methods for the vibration response of and acoustic radiation from a periodical orthogonally rib-stiffened plate. Chinese Journal of Acoustics. 2019(03): 309-330 . 必应学术
8.	周海安，王晓明，吴化勇，孟建兵，李丽君. 高效半解析方法分析周期正交加筋板的振动-声辐射特性. 声学学报. 2018(02): 224-238 . 百度学术
9.	张恺，纪刚，周其斗，李宗威. 基于统计能量法研究肋骨对双层圆柱壳声辐射特性的影响. 中国舰船研究. 2018(05): 46-52 . 百度学术
10.	徐中明，赖诗洋，郭庆，贺岩松. 汽车车内中高频噪声模拟仿真分析. 重庆理工大学学报(自然科学). 2017(06): 1-7 . 百度学术
11.	张武林，盛美萍. 不规则结构导纳参数建模方法研究. 噪声与振动控制. 2016(02): 27-30+45 . 百度学术
12.	周俊，饶柱石，塔娜. 周期结构带隙的能效观点. 噪声与振动控制. 2016(02): 1-5+45 . 百度学术

其他类型引用(18)

[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 物理学报 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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期刊类型引用(12)

1.	辛雨柯，邓庆田，宋学力，李新波. 加筋曲板结构抗弯承载能力分析. 塑性工程学报. 2024(02): 189-198 . 百度学术
2.	毛军喜，欧立新，孔德睿，陈韬，张迅. 钢混加强圈对钢波纹板裸拱涵动力特性的影响研究. 施工技术(中英文). 2024(18): 32-37 . 百度学术
3.	汤冬，马梓铜，张克澳，王汝鹏，辛松刚. 正交加筋板中板梁耦合动力特性. 中国舰船研究. 2023(04): 265-275 . 百度学术
4.	马天兵，丁威海，周青，杜菲. 基于改进滑模变结构的加筋板振动控制研究. 安徽理工大学学报(自然科学版). 2021(01): 7-12 . 百度学术
5.	孔德睿，张迅，刘子琦，游颖川，郑宁哲，周靖翔. 基于颗粒阻尼的U肋加劲板减振降噪初探. 噪声与振动控制. 2021(05): 38-44 . 百度学术
6.	周海安，修孝廷，孟建兵. 基于有限元/边界元的双层周期加筋板声辐射分析. 山东理工大学学报(自然科学版). 2019(03): 31-36+42 . 百度学术
7.	ZHOU Haian，WANG Xiaoming，WU Huayong，MENG Jianbing，LI Lijun. Efficient semi-analytical methods for the vibration response of and acoustic radiation from a periodical orthogonally rib-stiffened plate. Chinese Journal of Acoustics. 2019(03): 309-330 . 必应学术
8.	周海安，王晓明，吴化勇，孟建兵，李丽君. 高效半解析方法分析周期正交加筋板的振动-声辐射特性. 声学学报. 2018(02): 224-238 . 百度学术
9.	张恺，纪刚，周其斗，李宗威. 基于统计能量法研究肋骨对双层圆柱壳声辐射特性的影响. 中国舰船研究. 2018(05): 46-52 . 百度学术
10.	徐中明，赖诗洋，郭庆，贺岩松. 汽车车内中高频噪声模拟仿真分析. 重庆理工大学学报(自然科学). 2017(06): 1-7 . 百度学术
11.	张武林，盛美萍. 不规则结构导纳参数建模方法研究. 噪声与振动控制. 2016(02): 27-30+45 . 百度学术
12.	周俊，饶柱石，塔娜. 周期结构带隙的能效观点. 噪声与振动控制. 2016(02): 1-5+45 . 百度学术

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