分数导数模型描述的饱和土桩纵向振动分析
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摘要
土体具有黏弹性性质,为了更好地考虑饱和土体固相土骨架的黏弹性性质,在分数导数理论和多孔介质理论的基础上,将土体视为液固饱和两相介质,并利用分数导数模型来描述饱和土固相土骨架的应力-应变关系,建立分数导数模型描述的饱和土的控制方程。在三维轴对称情况下,利用势函数和分离变量法研究了分数导数模型描述的饱和土中桩的振动问题。分析了模型参数对饱和土中桩的竖向振动的影响。研究表明,分数导数模型描述的饱和土的控制方程应用范围更广,模型参数对桩的竖向振动有较大的影响。
As we know,the soil has viscoelastic characteristic,the control equations of saturated soil described by fractional derivative model are established based on the theories of porous media and theories of fractional derivatives,in which the soil is regarded as porous medium filled with water;and the stress-strain relationship is described by fractional derivative viscoelastic model for considering the viscoelastic properties of soil skeleton.The vertical coupled vibration of a pile in a saturated soil described by fractional derivative model is investigated by introducing the potential functions and separation of variables method under the three-dimensional axisymmetric condition;and the influences of the model parameters on the vertical vibration of a pile in saturated soil is analyzed.The results indicate that the control equations of the saturated soil described by fractional derivative model has a wider application;and the model parameters has great influences on the vertical vibration of a pile in saturated soil.
As we know,the soil has viscoelastic characteristic,the control equations of saturated soil described by fractional derivative model are established based on the theories of porous media and theories of fractional derivatives,in which the soil is regarded as porous medium filled with water;and the stress-strain relationship is described by fractional derivative viscoelastic model for considering the viscoelastic properties of soil skeleton.The vertical coupled vibration of a pile in a saturated soil described by fractional derivative model is investigated by introducing the potential functions and separation of variables method under the three-dimensional axisymmetric condition;and the influences of the model parameters on the vertical vibration of a pile in saturated soil is analyzed.The results indicate that the control equations of the saturated soil described by fractional derivative model has a wider application;and the model parameters has great influences on the vertical vibration of a pile in saturated soil.
引文
[1]NOGAMI T,NOVAK M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering Structural Dynamics,1976,4:277-293.
[2]NOVAK M,NOGAMI T,ABOUL ELLA F.Dynamic soil reactions for plane strain case[J].Journal of Engineering Mechanics,1978,104(EM4):953-959.
[3]NOGAMI T,KONAGAI K.Time domain axial response of dynamically loaded single piles[J].Journal of Engineering Mechanics,1986,12(11):1241-1252.
[4]ZENG X,RAJAPAKSE RKND.Dynamic axial load transfer from elastic bar to poroelastic medium[J].Journal of Engineering Mechanics Division,ASCE,1999,125(9):1048-1055.
[5]JIN B,ZHOU D,ZHONG Z.Lateral dynamic compliance of pile embedded in poroelastic half space[J].Soil Dynamics and Earthquake Engineering,2001,21:519-525.
[6]ORLANDO MAESO,JUAN J,AZNAREZ,et al,Dynamic impedances of piles and groups of piles in saturated soils[J].Computers&Structures,2005,83:769-782
[7]李强,王奎华,谢康和.饱和土中端承桩纵向振动特性研究[J].力学学报,2004,36(4):435-442.LI Qing,WANG Kui-hua,XIE Kang-he.Vertical vibration of an end bearing pile embedded in saturated soil[J].Acta Mechanical Sinica,2004,36(4):435-442.
[8]陆建飞.频域内半空间饱和土中水平受荷桩的动力分析[J].岩石力学与工程学报,2002,21(4):577-581.LU Jian-fei.Dynamic frequency domain analysis of laterally loaded pile in saturated soil[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(4):577-581.
[9]张玉红,黄义.二相介质饱和土中群桩动力阻抗分析[J].地震工程与工程振动,2001,21(3):113-116.ZHANG Yu-hong,HUANG Yi.Dynamic impedance of group piles in two-phase fluid-saturated soils[J].Earthquake Engineering and Engineering Vibration,2001,21(3):113-116.
[10]EDELMAN I,WILMANSKI K.Asymptotic analysis of surface waves at vacuum/porous medium and liquid/porous medium interfaces[J].Continuum Mechanics and Thermodynamics,2002,14:25-44.
[11]刘林超,张卫.具有分数Kelvin模型的黏弹性岩体中水平圆形硐室的变形特性[J].岩土力学,2005,26(2):287-289.LIU Lin-chao,ZHANG Wei.The deformation proprieties of horizontal round adits in viscoelastic rocks by fractional Kelvin model[J].Rock and Soil Mechanics,2005,26(2):287-289.
[12]DE BOER,LIU R Z.Propagation of acceleration waves in incompressible saturated porous solids[J].Transport in Porous Media,1994,21:163-173.
[13]ROSSIKHIN Y A,SHITIKOTA M V.Applicitions of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids[J].Applied Mechanics Reviews,1997,50(1):15-67.
[2]NOVAK M,NOGAMI T,ABOUL ELLA F.Dynamic soil reactions for plane strain case[J].Journal of Engineering Mechanics,1978,104(EM4):953-959.
[3]NOGAMI T,KONAGAI K.Time domain axial response of dynamically loaded single piles[J].Journal of Engineering Mechanics,1986,12(11):1241-1252.
[4]ZENG X,RAJAPAKSE RKND.Dynamic axial load transfer from elastic bar to poroelastic medium[J].Journal of Engineering Mechanics Division,ASCE,1999,125(9):1048-1055.
[5]JIN B,ZHOU D,ZHONG Z.Lateral dynamic compliance of pile embedded in poroelastic half space[J].Soil Dynamics and Earthquake Engineering,2001,21:519-525.
[6]ORLANDO MAESO,JUAN J,AZNAREZ,et al,Dynamic impedances of piles and groups of piles in saturated soils[J].Computers&Structures,2005,83:769-782
[7]李强,王奎华,谢康和.饱和土中端承桩纵向振动特性研究[J].力学学报,2004,36(4):435-442.LI Qing,WANG Kui-hua,XIE Kang-he.Vertical vibration of an end bearing pile embedded in saturated soil[J].Acta Mechanical Sinica,2004,36(4):435-442.
[8]陆建飞.频域内半空间饱和土中水平受荷桩的动力分析[J].岩石力学与工程学报,2002,21(4):577-581.LU Jian-fei.Dynamic frequency domain analysis of laterally loaded pile in saturated soil[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(4):577-581.
[9]张玉红,黄义.二相介质饱和土中群桩动力阻抗分析[J].地震工程与工程振动,2001,21(3):113-116.ZHANG Yu-hong,HUANG Yi.Dynamic impedance of group piles in two-phase fluid-saturated soils[J].Earthquake Engineering and Engineering Vibration,2001,21(3):113-116.
[10]EDELMAN I,WILMANSKI K.Asymptotic analysis of surface waves at vacuum/porous medium and liquid/porous medium interfaces[J].Continuum Mechanics and Thermodynamics,2002,14:25-44.
[11]刘林超,张卫.具有分数Kelvin模型的黏弹性岩体中水平圆形硐室的变形特性[J].岩土力学,2005,26(2):287-289.LIU Lin-chao,ZHANG Wei.The deformation proprieties of horizontal round adits in viscoelastic rocks by fractional Kelvin model[J].Rock and Soil Mechanics,2005,26(2):287-289.
[12]DE BOER,LIU R Z.Propagation of acceleration waves in incompressible saturated porous solids[J].Transport in Porous Media,1994,21:163-173.
[13]ROSSIKHIN Y A,SHITIKOTA M V.Applicitions of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids[J].Applied Mechanics Reviews,1997,50(1):15-67.
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