关于两相饱和介质中流相Green函数的解析解
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摘要
自然界中许多动力学问题需要用两相饱和介质Green函数求得解答,本文在两相饱和介质位移场Green函数解答的基础上,求得的有关饱和流体孔隙压力,进、排流体流量等三个Green函数.从而使两相饱和介质涉及流体问题的Lamb方程能完整地使用.论文在推导过程中详细地阐述了流体三个Green函数的物理意义,并将所得结果与Chen(1994)的纯数学的结果作了了对比.最后文章讨论了解析解的稳定性.
A large number of kinetic problems in nature need to employ the Green function of two-phase saturated medium for solutions.In this paper the authors based on the displacement Green function of two-phase saturated medium,and obtained three relevant Green functions of saturated fluid for the pressure of pore,the flux of fluid inflow or outflow respectively.Thereby, Lamb integral equation of two-phase saturated medium can be applied completely.In the process of derivation the physical significance of three Green functions of fluid phase is expounded elaborately and in detail.Moreover,the results of this paper are compared with Chen's results (1994) which are purely mathematical.There is a discussion on the stability of solutions at the end of the paper.
A large number of kinetic problems in nature need to employ the Green function of two-phase saturated medium for solutions.In this paper the authors based on the displacement Green function of two-phase saturated medium,and obtained three relevant Green functions of saturated fluid for the pressure of pore,the flux of fluid inflow or outflow respectively.Thereby, Lamb integral equation of two-phase saturated medium can be applied completely.In the process of derivation the physical significance of three Green functions of fluid phase is expounded elaborately and in detail.Moreover,the results of this paper are compared with Chen's results (1994) which are purely mathematical.There is a discussion on the stability of solutions at the end of the paper.
引文
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[2] Madariage R,Olsen K,Archuleta K.Modeling dynamic rupture in a 3D earthquake fault model.Bull Seism Soc Amer,1998,88(5) :1182～1197
[3] Oreste P P.The importance of longitudinal stress effects on the static conditions of the final lining of a tunnel.Tunnelling and Underground Space Technology,2002,1(17) :21～32
[4] Quentin G,Salah N,Alexandre W.On the transmission of transient elastodynamic waves at a frictionless contact interface:application to a weakly coupled bionmaterial.International Journal of Solids and Structures,2004,2(41) :459～480
[5] Luccio F D,Fukuyama E,Pino N A.The 2002 Molise earthquake sequence:What can we learn about the tectonics of southern Italy.Tectonophysics,2005,405:141～154
[6] Sen R,Davies T G,Banerjee P K.Dynamic analysis of piles and pile groups embedded in homogeneous soils.Earthquake Eng Struct Dyn,1985,13:53～65
[7] ThamL G.Chu C K,Lei Z X.Analysis of the transient responsé of vertically loaded single piles by time-domain BEM.Computers and Geotechnics,1996,2(19) :117～136
[8] Dimitris L,Karabalis,Mohsen Mohammadi.3-D dynamic foundation-soil-foundation interaction on layered soil.Soil Dynamics and Earthquake Engineering,1998,3(17) :139～152
[9] Celebi E.Three-dimensional modelling of train-track and subsoil analysis for surface vibrations due to moving loads.Applied Mathematics and Computation,2006,1(179) :209～230
[10] Galvin P,Dominguez J.High speed train induced ground motion and interaction with structures.Journal of Sound and Vibration,2007,307:755～777
[11] Bode C,Hirschauer R,Savidis S A. Soil structure interaction in the time domain using halfspace Green's functions.Soil Dynamics and Earthquake Engineering,2002,4(22) :283～295
[12] Bierer T,Bode C.A semi analytical model in time domain for moving loads.Soil Dynamics and Earthquake Engineering,2007,12(27) :1073～1081
[13] 丁伯阳,樊良本,吴建华.两相饱和介质中的集中力点源位移场解与应用.地球物理学报,1 999,42(6) :800～808 Ding B Y,Fan L B,Wu J H.The Green function and wave field on two-phase saturated medium by concentrated force.Chinese J.Geophys.(in Chinese),1999,42(6) :800～808
[14] Ding B Y,Fan L B,Wu J H.A solution for displacement field of point source of concentrated force in saturated twophase medium and its application.Chinese J.Geophys.,2000,43(1) :141～148
[15] 丁伯阳,丁翠红,孟凡丽.集中力作用下的两相饱和介质位移场Green函数.力学学报,2001,33(2) :234～241
Ding B Y,Ding C H,Meng F L.The Green function on twophase saturated medium by concentrated force.Acta Mechanica Sinica(in Chinese),2001,33(2) :234～241
[16] Ding B Y,Meng F L,Hu M Y.The source vector and static displacement field by elastic dislocation on the two-phase saturated medium.Acta Seis Mologica Sinica,14(3) :251～258
[17] 丁伯阳,樊良本,孟繁丽等.两相饱和介质半无限空间的位错位移场.地球物理学报.2003,46(3) :408～414 Ding B Y,Fan L B,Meng F L,et al.The displacement field of dislocation on the half-space of two-phase saturated medium.Chinese J.Geophys.(in Chinese),2003,46(3) :408～414
[18] Ding B Y,Ding C H,Chen Y.Green function on two-phase saturated medium by concentrated force in two-dimensional displacement field.App.Math.Mech.,2004,25(8) .:951～956
[19] Chen J..Time domain fundamental solution to Boit's complete equations of dynamic poroelasticity Part Ⅰ.Int.J.Solid Struct.,1994,31:1447～1490
[20] Chen J.Time domain fundamental solution to Boit's complete equations of dynamic poroelasticity Part Ⅱ.Int.J.Solid Struct.,1994,31:169～202
[21] Biot M A.Theory of propagation of elastic wave in a fluidsaturated soil.J.Acoust.Soc.Amer.,1956,28:168～178
[22] Eringen A C,Sububi E S.Electrodynamics.Vol.2 Liner theory.Academic Press New York.San-Francisco.London,1975． 76～138
[23] 刘银斌,李幼铭,吴如山.横向各向同性多孔介质中的地震波传播.地球物理学报,1994,37:499～514 Liu Y B,Li Y M,Wu R S.Seismic wave propagation in transversely isotropic porous media.Chinese J.Geophys.(in Chinese),1994,37:499～514
[24] Bonnet G.Basic singular solutions for a poroelastic medium in the dynamic range.J.Acoust.Soc.Amer.,1987,82 1758～1762
[2] Madariage R,Olsen K,Archuleta K.Modeling dynamic rupture in a 3D earthquake fault model.Bull Seism Soc Amer,1998,88(5) :1182～1197
[3] Oreste P P.The importance of longitudinal stress effects on the static conditions of the final lining of a tunnel.Tunnelling and Underground Space Technology,2002,1(17) :21～32
[4] Quentin G,Salah N,Alexandre W.On the transmission of transient elastodynamic waves at a frictionless contact interface:application to a weakly coupled bionmaterial.International Journal of Solids and Structures,2004,2(41) :459～480
[5] Luccio F D,Fukuyama E,Pino N A.The 2002 Molise earthquake sequence:What can we learn about the tectonics of southern Italy.Tectonophysics,2005,405:141～154
[6] Sen R,Davies T G,Banerjee P K.Dynamic analysis of piles and pile groups embedded in homogeneous soils.Earthquake Eng Struct Dyn,1985,13:53～65
[7] ThamL G.Chu C K,Lei Z X.Analysis of the transient responsé of vertically loaded single piles by time-domain BEM.Computers and Geotechnics,1996,2(19) :117～136
[8] Dimitris L,Karabalis,Mohsen Mohammadi.3-D dynamic foundation-soil-foundation interaction on layered soil.Soil Dynamics and Earthquake Engineering,1998,3(17) :139～152
[9] Celebi E.Three-dimensional modelling of train-track and subsoil analysis for surface vibrations due to moving loads.Applied Mathematics and Computation,2006,1(179) :209～230
[10] Galvin P,Dominguez J.High speed train induced ground motion and interaction with structures.Journal of Sound and Vibration,2007,307:755～777
[11] Bode C,Hirschauer R,Savidis S A. Soil structure interaction in the time domain using halfspace Green's functions.Soil Dynamics and Earthquake Engineering,2002,4(22) :283～295
[12] Bierer T,Bode C.A semi analytical model in time domain for moving loads.Soil Dynamics and Earthquake Engineering,2007,12(27) :1073～1081
[13] 丁伯阳,樊良本,吴建华.两相饱和介质中的集中力点源位移场解与应用.地球物理学报,1 999,42(6) :800～808 Ding B Y,Fan L B,Wu J H.The Green function and wave field on two-phase saturated medium by concentrated force.Chinese J.Geophys.(in Chinese),1999,42(6) :800～808
[14] Ding B Y,Fan L B,Wu J H.A solution for displacement field of point source of concentrated force in saturated twophase medium and its application.Chinese J.Geophys.,2000,43(1) :141～148
[15] 丁伯阳,丁翠红,孟凡丽.集中力作用下的两相饱和介质位移场Green函数.力学学报,2001,33(2) :234～241
Ding B Y,Ding C H,Meng F L.The Green function on twophase saturated medium by concentrated force.Acta Mechanica Sinica(in Chinese),2001,33(2) :234～241
[16] Ding B Y,Meng F L,Hu M Y.The source vector and static displacement field by elastic dislocation on the two-phase saturated medium.Acta Seis Mologica Sinica,14(3) :251～258
[17] 丁伯阳,樊良本,孟繁丽等.两相饱和介质半无限空间的位错位移场.地球物理学报.2003,46(3) :408～414 Ding B Y,Fan L B,Meng F L,et al.The displacement field of dislocation on the half-space of two-phase saturated medium.Chinese J.Geophys.(in Chinese),2003,46(3) :408～414
[18] Ding B Y,Ding C H,Chen Y.Green function on two-phase saturated medium by concentrated force in two-dimensional displacement field.App.Math.Mech.,2004,25(8) .:951～956
[19] Chen J..Time domain fundamental solution to Boit's complete equations of dynamic poroelasticity Part Ⅰ.Int.J.Solid Struct.,1994,31:1447～1490
[20] Chen J.Time domain fundamental solution to Boit's complete equations of dynamic poroelasticity Part Ⅱ.Int.J.Solid Struct.,1994,31:169～202
[21] Biot M A.Theory of propagation of elastic wave in a fluidsaturated soil.J.Acoust.Soc.Amer.,1956,28:168～178
[22] Eringen A C,Sububi E S.Electrodynamics.Vol.2 Liner theory.Academic Press New York.San-Francisco.London,1975． 76～138
[23] 刘银斌,李幼铭,吴如山.横向各向同性多孔介质中的地震波传播.地球物理学报,1994,37:499～514 Liu Y B,Li Y M,Wu R S.Seismic wave propagation in transversely isotropic porous media.Chinese J.Geophys.(in Chinese),1994,37:499～514
[24] Bonnet G.Basic singular solutions for a poroelastic medium in the dynamic range.J.Acoust.Soc.Amer.,1987,82 1758～1762
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