半空间饱和孔隙介质在P、SV波入射下的波场解
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摘要
基于Biot理论,利用Fourier变换和势函数方法,将Biot波动方程化为一组Helmholtz方程。通过入射波和反射波的波势函数表达式及边界条件,可得波势函数的幅值,进而可得位移、应力、孔压。数值算例给出了P和SV波入射的波场解及其随饱和孔隙介质参数的变化。本文的结果是研究饱和土在地震波作用下土的液化以及利用积分方程或边界元方法研究桩在地震波作用下的动力响应的基础。
Based on Biot′s theory,using Fourier transform and potential function,the wave dynamic equations for Biot′s theory can be deduced to several Helmholtz equations.The amplitudes of the potentials function can be determined using the expression formula for the potential function of incident wave and reflected wave and the boundary conditions.Then the displacement,the stresses and the pore pressure can be calculated.By numerical examples wave field solution for the incident P and SV waves and their chang with the parameters of saturated porous medium are presented in the paper.The results are basis of the liquefaction for a saturated soil under the action of seisimic waves.Also,it is crucial for the solution of the pile dynamic response problem by integral equation method and boundary elelment method numerical solution under the action of seismic waves.
Based on Biot′s theory,using Fourier transform and potential function,the wave dynamic equations for Biot′s theory can be deduced to several Helmholtz equations.The amplitudes of the potentials function can be determined using the expression formula for the potential function of incident wave and reflected wave and the boundary conditions.Then the displacement,the stresses and the pore pressure can be calculated.By numerical examples wave field solution for the incident P and SV waves and their chang with the parameters of saturated porous medium are presented in the paper.The results are basis of the liquefaction for a saturated soil under the action of seisimic waves.Also,it is crucial for the solution of the pile dynamic response problem by integral equation method and boundary elelment method numerical solution under the action of seismic waves.
引文
1 Paria G.Flow of fluid through porous deformable solids.Appl.Mech.Rec.1963,16:421-423
2 de.Boer,R.Ehlers,W.Historical review of the formulation ofporous media theories.Acra Mechanica,1988,10(74):1-8
3 Zeng X,Rajapakse,R.K.N.D.Dynamic axial load transfer fromelastic bar to poroelastic medium.Eng Mech,1999,125(9):1048-1055
4 Jin B,Zhou D,Zhong Z.Lateral dynamic compliance of pileembedded in poroelastic half space.Soil Dynamic and Earth-quake Eng,2001,21:518-525
5王建华,陆建飞,沈为平.半空间饱和土在内部简谐垂直力作用下的Green函数.水利学报,2001,(3):25-28
6陈胜立,张建民,陈龙珠.饱和土埋置力源的三维动力Lame问题解答.固体力学学报,2004,25:149-154
7王立忠.吴世明.波在饱和土中传播的若干问题.岩土工程学报,1995,17(6):96-101.
8杨峻.地震波在饱和土层界面的反射与透射.地震学报,1997,19(1):19-35
9 Biot MA.Theory of propagation of elastic waves in a fluid-satu-rated porous solid,I:Low frenquency range.Journal of theAcoustical Society of America,1956,28:168-178
10 Biot MA.Theory of propagation of elastic waves in a fluid-satu-rated porous solid,II:Higher frequency range.Journal of theAcoustical Society of America,1956,28:179-191
11 Biot MA.Mechanics of deformation and acoustic propagation inporous media.Journal of Applied Physics,1962,33:1482-1498
12 Biot MA.General theory of three-dimensional consolidation.Journal of Applied Physics,1956,12:155-164
13 Zimmerman C,Stern M.Boundary element solution of 3Dwave scatter problems in a poroelastic medium.EngineeringAnalysis with Boundary Elements,1993,12:223-240
14 Bonnet G.Basic singular solutions for poroelastic medium in thedynamic range.Journal of the Acoustical Society of America,1987,82:1758-1762
15 Auld B A.Ascoustic fields and waves in solids.New York,Wiley,1973
2 de.Boer,R.Ehlers,W.Historical review of the formulation ofporous media theories.Acra Mechanica,1988,10(74):1-8
3 Zeng X,Rajapakse,R.K.N.D.Dynamic axial load transfer fromelastic bar to poroelastic medium.Eng Mech,1999,125(9):1048-1055
4 Jin B,Zhou D,Zhong Z.Lateral dynamic compliance of pileembedded in poroelastic half space.Soil Dynamic and Earth-quake Eng,2001,21:518-525
5王建华,陆建飞,沈为平.半空间饱和土在内部简谐垂直力作用下的Green函数.水利学报,2001,(3):25-28
6陈胜立,张建民,陈龙珠.饱和土埋置力源的三维动力Lame问题解答.固体力学学报,2004,25:149-154
7王立忠.吴世明.波在饱和土中传播的若干问题.岩土工程学报,1995,17(6):96-101.
8杨峻.地震波在饱和土层界面的反射与透射.地震学报,1997,19(1):19-35
9 Biot MA.Theory of propagation of elastic waves in a fluid-satu-rated porous solid,I:Low frenquency range.Journal of theAcoustical Society of America,1956,28:168-178
10 Biot MA.Theory of propagation of elastic waves in a fluid-satu-rated porous solid,II:Higher frequency range.Journal of theAcoustical Society of America,1956,28:179-191
11 Biot MA.Mechanics of deformation and acoustic propagation inporous media.Journal of Applied Physics,1962,33:1482-1498
12 Biot MA.General theory of three-dimensional consolidation.Journal of Applied Physics,1956,12:155-164
13 Zimmerman C,Stern M.Boundary element solution of 3Dwave scatter problems in a poroelastic medium.EngineeringAnalysis with Boundary Elements,1993,12:223-240
14 Bonnet G.Basic singular solutions for poroelastic medium in thedynamic range.Journal of the Acoustical Society of America,1987,82:1758-1762
15 Auld B A.Ascoustic fields and waves in solids.New York,Wiley,1973
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