分数导数粘弹性土层模型中桩基竖向振动特性研究
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摘要
粘弹土体的应力-应变关系利用分数导数粘弹性模型进行描述,建立了分数导数粘弹性土层的竖向振动控制方程。在考虑三维波动的条件下,利用势函数和分离变量的方法求解了分数导数粘弹性土层的竖向振动。考虑桩土边界条件和接触条件对分数导数粘弹性土中桩基的竖向振动进行了研究,分析了主要桩土力学参数对桩顶复刚度和导纳的影响规律。研究表明:分数导数的阶数、土体模型参数和桩长径比对桩顶复刚度和导纳有较大影响;分数导数粘弹性模型可以在较大的范围内较精确地描述土体的力学行为;当长径比增大到一定的程度时再增加长径比对桩基竖向振动特性的影响不大。
The paper established the vertical dynamic governing equations of viscoelastic soil,where the stress-strain relationship of soil is described by fractional derivative viscoelastic model.Considering the three-dimensional wave effect of the soil-pile,the vertical vibration of soil described by fractional derivative viscoleastic model is solved by potential functions and the method of separation variables.The vertical coupled vibration of a pile in viscoleastic soil is investigated with boundary and contact conditions.The influences of mechanical parameters of pile and soil on the vertical vibration of a pile in viscoelastic soil are also analyzed.The results indicate that the order of fractional derivative,the model parameters of soil and the length-radius ratio have great impact on the complex stiffness and admittance at pile head;and the fractional derivative viscoelastic model can describe the mechanical behavior more accurately in larger range;and moreover,the influence of length-radius ratio becomes very smaller when the length-radius ratio increases to a certain value..
The paper established the vertical dynamic governing equations of viscoelastic soil,where the stress-strain relationship of soil is described by fractional derivative viscoelastic model.Considering the three-dimensional wave effect of the soil-pile,the vertical vibration of soil described by fractional derivative viscoleastic model is solved by potential functions and the method of separation variables.The vertical coupled vibration of a pile in viscoleastic soil is investigated with boundary and contact conditions.The influences of mechanical parameters of pile and soil on the vertical vibration of a pile in viscoelastic soil are also analyzed.The results indicate that the order of fractional derivative,the model parameters of soil and the length-radius ratio have great impact on the complex stiffness and admittance at pile head;and the fractional derivative viscoelastic model can describe the mechanical behavior more accurately in larger range;and moreover,the influence of length-radius ratio becomes very smaller when the length-radius ratio increases to a certain value..
引文
[1]Nogami T,Novak M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering and Structural Dynamics,1976,4:277―293.
[2]Novak M,Nogami T,Aboul-Ella F.Dynamic soil reactions for plane strain case[J].Jounal of Engineering Mechanics,1978,104(4):953―959.
[3]Nogami T,Konagai K.Time domain axial response of dynamically loaded single piles[J].Jounal of Engineering Mechanics,1986,112(11):1241―1252.
[4]Mamoon S M,Kaynia A M,Banerjee P K.Frequency-domain dynamic analysis of piles and pile groups[J].Jounal of Engineering Mechanics,1990,116(10):2237―2257.
[5]Novak M.Dynamic stiffness and damping of piles[J].Canadian Geotechnical Journal,1974,11:574―598.
[6]胡昌斌,黄晓明.成层粘弹性土中桩土耦合纵向振动时域响应研究[J].地震工程与工程振动,2006,26(4):205―211.Hu Changbin,Huang Xiaoming.A quasi-analytical solution to soil-pile interaction in longitudinal vibration in layered soils considering vertical wave effect on soils[J].Earthquake Engineering and Engineering Vibration,2006,26(4):205―211.(in Chinese)
[7]周绪红,蒋建国,邹银生.粘弹性介质中考虑轴力作用时桩的动力分析[J].土木工程学报,2005,38(2):87―91.Zhou Xuhong,Jiang Jianguo,Zou Yinsheng.Dynamic analysis of piles under axial loading and lateral dynamic force in visco-elastic medium[J].China Civil Engineering Journal,2005,38(2):87―91.(in Chinese)
[8]刘林超,张卫.具有分数Kelvin模型的粘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 Linchao,Zhang Wei.The deformation proprieties of horizontal round adits in viscoelastic rocks by fractional Kelvin model[J].Rock and Soil Mechanicals,2005,26(2):287―289.(in Chinese)
[9]Bagley R L,Torvik P J.A theoretical basis for the application of fractional calculus to viscoelasticity[J].Journal of Rheology,1983,27(3):201―210.
[10]Zhu Zhengyou,Li Genguo,Chen Changjun.Quasi-static and dynamical analysis for viscoelastic Timoshenko beam with fractional derivative constitutive relation[J].Applied Mathematics and Mechanics,2002,23(1):1―7.
[11]Miller K S,Ross B.An introduction to the fractional calculus and fractional differential equations[M].New York:John Wiley&Sons,1993.
[2]Novak M,Nogami T,Aboul-Ella F.Dynamic soil reactions for plane strain case[J].Jounal of Engineering Mechanics,1978,104(4):953―959.
[3]Nogami T,Konagai K.Time domain axial response of dynamically loaded single piles[J].Jounal of Engineering Mechanics,1986,112(11):1241―1252.
[4]Mamoon S M,Kaynia A M,Banerjee P K.Frequency-domain dynamic analysis of piles and pile groups[J].Jounal of Engineering Mechanics,1990,116(10):2237―2257.
[5]Novak M.Dynamic stiffness and damping of piles[J].Canadian Geotechnical Journal,1974,11:574―598.
[6]胡昌斌,黄晓明.成层粘弹性土中桩土耦合纵向振动时域响应研究[J].地震工程与工程振动,2006,26(4):205―211.Hu Changbin,Huang Xiaoming.A quasi-analytical solution to soil-pile interaction in longitudinal vibration in layered soils considering vertical wave effect on soils[J].Earthquake Engineering and Engineering Vibration,2006,26(4):205―211.(in Chinese)
[7]周绪红,蒋建国,邹银生.粘弹性介质中考虑轴力作用时桩的动力分析[J].土木工程学报,2005,38(2):87―91.Zhou Xuhong,Jiang Jianguo,Zou Yinsheng.Dynamic analysis of piles under axial loading and lateral dynamic force in visco-elastic medium[J].China Civil Engineering Journal,2005,38(2):87―91.(in Chinese)
[8]刘林超,张卫.具有分数Kelvin模型的粘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 Linchao,Zhang Wei.The deformation proprieties of horizontal round adits in viscoelastic rocks by fractional Kelvin model[J].Rock and Soil Mechanicals,2005,26(2):287―289.(in Chinese)
[9]Bagley R L,Torvik P J.A theoretical basis for the application of fractional calculus to viscoelasticity[J].Journal of Rheology,1983,27(3):201―210.
[10]Zhu Zhengyou,Li Genguo,Chen Changjun.Quasi-static and dynamical analysis for viscoelastic Timoshenko beam with fractional derivative constitutive relation[J].Applied Mathematics and Mechanics,2002,23(1):1―7.
[11]Miller K S,Ross B.An introduction to the fractional calculus and fractional differential equations[M].New York:John Wiley&Sons,1993.
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