横观各向同性饱和地基的稳态动力响应分析
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摘要
基于双重Fourier变换技术,在直角坐标系下求解了横观各向同性饱和地基的三维Biot动力方程,得到地基位移分量、孔隙流体压力和总应力分量的积分形式一般解。继而利用一般解研究了横观各向同性饱和地基在任意分布的表面谐振力作用下的动力响应问题。
A study of the harmonic responses of transversely isotropic saturated subsoil under a circular non-axisymmetrical harmonic source has been presented in recent paper by the authors using the technique of Fourier expansion and Hankel transformation.However,the method may not always by valid.In this paper,the work is extended to the case of general harmonic source distributing on arbitrary surface zone on the half-space with transversely isotropic saturated subsoil.Based on the Biot's theory and by the technique of double Fourier transformation,the governing differential equations for transversely isotropic asturated soils are easily solved and the solutions of stress and displacement in Fourier transformed zone are obtained.Then,under the boundary conditions,the analytical solutions of harmonic response for subsoil are presented.
A study of the harmonic responses of transversely isotropic saturated subsoil under a circular non-axisymmetrical harmonic source has been presented in recent paper by the authors using the technique of Fourier expansion and Hankel transformation.However,the method may not always by valid.In this paper,the work is extended to the case of general harmonic source distributing on arbitrary surface zone on the half-space with transversely isotropic saturated subsoil.Based on the Biot's theory and by the technique of double Fourier transformation,the governing differential equations for transversely isotropic asturated soils are easily solved and the solutions of stress and displacement in Fourier transformed zone are obtained.Then,under the boundary conditions,the analytical solutions of harmonic response for subsoil are presented.
引文
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[10]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[J].地球物理学报,1994,37(4):499-514.
[11]汪越胜,章梓茂.横观各向同性液体饱和多孔介质中平面波的传播[J].力学学报,1997,29(30):257-268.
[12]胡亚元,王立忠.横观各向同性饱和土体的实用波动方程[J].振动工程学报,1998,12(2):170-176.
[13]BedfordA,CostleyRD,SternM.OnthedragandvirtualmasscoefficientsinBiot'sequations[J].JAcoustSocAm,1984,76(6):1804-1809.
[14]AuriaultJL,BorneL,ChambonR.Dynamicsofporoussaturatedmedia,checkingofgeneralizedlawofdarcy[J].JAcoustSocAm,1985,77(5):1641-1950.
[15]JohmisonDL.Theoryofdynamicpermeabilityandtortuosityinfluid-saturatedporousmedia[J].JfluidMech,1987,176:379-402.
[16]Kazi-Aoual,GuyBonnet,PaulJouanna.Green'sfounctioninaninfinitetransverselyisotropicsaturatedporoelasticmedium[J].JAcoustSocAm,1988,84(5):1883-1889
[2]LucoJE,WestmannRA.Dynamicresponseofcircularfootings[J].JEngMechDiv,ASCE,1971,97:1381-1395.
[3]BiotMA.Thetheoryofpropagationofelasticwavesinfluid-saturatedporoussolid[J].JAcoustSocAm,1956,28(2):168-191.
[4]BiotMA.Generaltheoryofacousticpropagationinporousdissipativemedia[J].JAcoustSocAm,1962,34(9):1254-1264.
[5]BiotMA.Mechanicsofdeformationandacousticpropagationinporousmedia[J].JApplPhys,1962,33(4):1482-1498.
[6]BadieyM,YamamotoT.Propagationofacousticnormalmodesinahomogeneousoceanoverlyinglayeredanisotropicporousbeds[J].JAcoustSocAm,1987,82(1):342-353.
[7]SchmittPD.Acousticmultipoleloggingintransverselyisotropicporoelasticformations[J].JAcoustSocAm,1989,86(6):2397-2421.
[8]Kazi-Aoual,GuyBonnet,PaulJouanna.Green'sfounctioninaninfinitetransverselyisotropicsaturatedporoelasticmedium[J].JAcoustSocAm,1988,84(5):1883-1889.
[9]SharmaMD,GognaML.Wavepropagationintransverselyisotropicliquid-saturatedporoussoids[J].JAcoustSocAm,1991,90(2):PartI:1068-1073.
[10]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[J].地球物理学报,1994,37(4):499-514.
[11]汪越胜,章梓茂.横观各向同性液体饱和多孔介质中平面波的传播[J].力学学报,1997,29(30):257-268.
[12]胡亚元,王立忠.横观各向同性饱和土体的实用波动方程[J].振动工程学报,1998,12(2):170-176.
[13]BedfordA,CostleyRD,SternM.OnthedragandvirtualmasscoefficientsinBiot'sequations[J].JAcoustSocAm,1984,76(6):1804-1809.
[14]AuriaultJL,BorneL,ChambonR.Dynamicsofporoussaturatedmedia,checkingofgeneralizedlawofdarcy[J].JAcoustSocAm,1985,77(5):1641-1950.
[15]JohmisonDL.Theoryofdynamicpermeabilityandtortuosityinfluid-saturatedporousmedia[J].JfluidMech,1987,176:379-402.
[16]Kazi-Aoual,GuyBonnet,PaulJouanna.Green'sfounctioninaninfinitetransverselyisotropicsaturatedporoelasticmedium[J].JAcoustSocAm,1988,84(5):1883-1889
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