Timoshenko模型桩水平振动的动力刚度
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摘要
基于桩-土相互作用的连续介质模型,利用桩的水平振动土阻抗结果,将桩等效为Timoshenko梁,研究线性黏弹性土层中Timoshenko模型端承桩水平振动的动力特性,给出频率域内桩头动力刚度的半解析解,得到动力刚度随频率的变化曲线.在此基础上研究物性和几何参数对刚度的影响,并与Euler-Bernoulli模型桩的结果进行比较.研究结果表明,端承桩水平振动的动态刚度受桩长细比、土软硬程度、水平激振频率等的影响,这些结果可以为工程设计提供参考.
Based on a continuum model of interaction between pile and soil,dynamic characteristics of horizontal vibration of a Timoshenko type end-bearing pile in a linear viscoelastic soil layer is studied by making the pile equivalent to a Timoshenko beam and using the existing results of soil resistance.Semi-analytical expressions of dynamic stiffness of the pile head is presented in the frequency domain.Variations of stiffness with respect to frequency are shown in terms of figures.Influences of the material and geometry parameters on stiffness are discussed.The results are compared with those obtained from the Euler-Bernoulli type model.It is shown that the dynamic stiffness of the end-bearing pile depends on the pile's slenderness ratio,soil property and excitation frequency.The results presented are useful in pile design.
Based on a continuum model of interaction between pile and soil,dynamic characteristics of horizontal vibration of a Timoshenko type end-bearing pile in a linear viscoelastic soil layer is studied by making the pile equivalent to a Timoshenko beam and using the existing results of soil resistance.Semi-analytical expressions of dynamic stiffness of the pile head is presented in the frequency domain.Variations of stiffness with respect to frequency are shown in terms of figures.Influences of the material and geometry parameters on stiffness are discussed.The results are compared with those obtained from the Euler-Bernoulli type model.It is shown that the dynamic stiffness of the end-bearing pile depends on the pile's slenderness ratio,soil property and excitation frequency.The results presented are useful in pile design.
引文
[1]NOVAK M.Piles under dynamic loads[C]∥Proceedingsof the 2nd International Conference on Recent Advancesin Geotechnical Earthquake Engineering and SoilDynamics.1991:2433-2457.
[2]NOVAK M.Dynamic stiffness and damping of piles[J].Canadian Geotechnical Journal,1974,11(4):574-598.
[3]NOVAK M,NOGAMI T.Soil-pile interaction in horizontalvibration[J].Earthquake Engineering and StructureDynamics,1977,5(3):263-281.
[4]李耀庄,李博.单桩水平及水平-摇摆耦合振动分析[J].世界地震工程,2006,22(4):160-165.
[5]NOGAMI T,NOVAK M.Coefficients of soil reaction topile vibration[J].Journal of Geotechnical EngineeringDivision,1980,106(5):565-570.
[6]NOGAMI T,OTANI J,KONAGAI K,et al.Nonlinearsoil-pile interaction model for dynamic lateral motion[J].Journal of Geotechnical Engineering,1992,118(1):89-106.
[7]EL NAGGER M H,NOVAK M.Nonlinear analysis fordynamic lateral pile response[J].Soil Dynamics andEarthquake Engineering,1996,15(4):233-244.
[8]CHAU K T,YANG X.Nonlinear interaction of soil-pilein horizontal vibration[J].Journal of EngineeringMechanics,2005,131(8):847-858.
[9]DAS Y C,SARGAND S M.Forced vibrations of laterallyloaded piles[J].International Journal of SolidStructure,1999,36(33):4975-4989.
[10]刘鑫,杨骁.悬浮桩水平振动的动力刚度[J].岩土力学,2008,29(4):1021-1026.
[11]MASOUMI H R,FRANCOIS S,DEGRANDE G.A non-linear coupled finite element-boundary element model forthe prediction of vibrations due to vibratory and impactpile driving[J].International Journal for Numerical andAnalytical Methods in Geomechanics,2009,33(2):245-274.
[12]NOGAMI T,REN F,CHEN J,et al.Vertical vibration ofpile in vibration-induced excess pore pressure field[J].Journal of Geotechnical and GeoenvironmentalEngineering,1997,123(5):422-429.
[13]ZENG X,RAJAPAKSE R K N D.Dynamic axial loadtransfer from elastic bar to poroelastic medium[J].Journal of Engineering Mechanics,1999,125(9):1048-1055.
[14]LU J F,JENG D S.Poroelastic model for pile-soilinteraction in a half-space porous medium due to seismicwaves[J].International Journal for Numerical andAnalytical Methods in Geomechanics,2008,32(1):1-41.
[15]余俊,尚守平,李忠,等.饱和土中端承桩水平振动动力响应分析[J].岩土工程学报,2009,31(3):408-415.
[16]HAN Y C.Study of vibrating foundations considering oil-pile-structure interaction for practical applications[J].Earthquake Engineering and Engineering Vibration,2008,7(3):321-327.
[17]JR WEAVER W,TIMOSHENKO S P,YOUNG D H.Vibration problems in engineering[M].Princeton:VanNostrand,1955:329-331.
[18]NOGAMI T,NOVAK M.Resistance of soil to ahorizontally vibrating pile[J].Earthquake Engineeringand Structure Dynamics,1977,5(3):247-261.
[2]NOVAK M.Dynamic stiffness and damping of piles[J].Canadian Geotechnical Journal,1974,11(4):574-598.
[3]NOVAK M,NOGAMI T.Soil-pile interaction in horizontalvibration[J].Earthquake Engineering and StructureDynamics,1977,5(3):263-281.
[4]李耀庄,李博.单桩水平及水平-摇摆耦合振动分析[J].世界地震工程,2006,22(4):160-165.
[5]NOGAMI T,NOVAK M.Coefficients of soil reaction topile vibration[J].Journal of Geotechnical EngineeringDivision,1980,106(5):565-570.
[6]NOGAMI T,OTANI J,KONAGAI K,et al.Nonlinearsoil-pile interaction model for dynamic lateral motion[J].Journal of Geotechnical Engineering,1992,118(1):89-106.
[7]EL NAGGER M H,NOVAK M.Nonlinear analysis fordynamic lateral pile response[J].Soil Dynamics andEarthquake Engineering,1996,15(4):233-244.
[8]CHAU K T,YANG X.Nonlinear interaction of soil-pilein horizontal vibration[J].Journal of EngineeringMechanics,2005,131(8):847-858.
[9]DAS Y C,SARGAND S M.Forced vibrations of laterallyloaded piles[J].International Journal of SolidStructure,1999,36(33):4975-4989.
[10]刘鑫,杨骁.悬浮桩水平振动的动力刚度[J].岩土力学,2008,29(4):1021-1026.
[11]MASOUMI H R,FRANCOIS S,DEGRANDE G.A non-linear coupled finite element-boundary element model forthe prediction of vibrations due to vibratory and impactpile driving[J].International Journal for Numerical andAnalytical Methods in Geomechanics,2009,33(2):245-274.
[12]NOGAMI T,REN F,CHEN J,et al.Vertical vibration ofpile in vibration-induced excess pore pressure field[J].Journal of Geotechnical and GeoenvironmentalEngineering,1997,123(5):422-429.
[13]ZENG X,RAJAPAKSE R K N D.Dynamic axial loadtransfer from elastic bar to poroelastic medium[J].Journal of Engineering Mechanics,1999,125(9):1048-1055.
[14]LU J F,JENG D S.Poroelastic model for pile-soilinteraction in a half-space porous medium due to seismicwaves[J].International Journal for Numerical andAnalytical Methods in Geomechanics,2008,32(1):1-41.
[15]余俊,尚守平,李忠,等.饱和土中端承桩水平振动动力响应分析[J].岩土工程学报,2009,31(3):408-415.
[16]HAN Y C.Study of vibrating foundations considering oil-pile-structure interaction for practical applications[J].Earthquake Engineering and Engineering Vibration,2008,7(3):321-327.
[17]JR WEAVER W,TIMOSHENKO S P,YOUNG D H.Vibration problems in engineering[M].Princeton:VanNostrand,1955:329-331.
[18]NOGAMI T,NOVAK M.Resistance of soil to ahorizontally vibrating pile[J].Earthquake Engineeringand Structure Dynamics,1977,5(3):247-261.
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