考虑桩体剪切变形的分数导数黏弹性土层中单桩水平振动
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摘要
建立了分数导数黏弹性(FDV)土层的水平振动控制方程,在Novak平面应变假定的基础上,求得FDV土体的水平动力等效刚度和阻尼.利用等效Winkler动力弹簧-阻尼器模型描述桩基和土体之间的动力相互作用,将桩体简化为Timoshenko梁模型,在同时考虑桩体弯曲和剪切变形的情况下建立了单桩水平振动的控制方程,求得了考虑桩体剪切变形的FDV土层中单桩的水平动力阻抗,讨论了分数导数的阶数、土体本构模型参数和桩体剪力形状系数对桩顶水平动力阻抗的影响.研究表明:对FDV土层中单桩的水平动力阻抗,采用Euler梁模型和Timoshenko梁模型得到的结果存在较大差异;分数导数的阶数主要对桩顶水平动力阻抗随频率变化曲线的峰值有的影响;FDV土体本构模型参数Tσ/Tε越小,桩顶的水平动力阻抗越大.桩体剪力变形系数对桩顶水平动力阻抗有较大影响.
The lateral vibration equations of the soil described by fractional derivative viscoelastic model are established.The lateral dynamic equivalent stiffness and damping of viscoelastic soil described by fractional derivative viscoelastic model are obtained on the basis of assumed surface strain of Novak.The dynamic interaction between pile and soil is described by equivalent Winkler dynamic spring-damping model,and the pile is simplified as Timoshenko model.The formula of lateral vibration of single pile is established by considering bending and shear deformation.The lateral dynamic impedance of single pile in soil is obtained by considering shear deformation.The influences of fractional derivative order,soil constitutive model parameters and shear shape factor of pile on lateral dynamic impedance are then investigated.It is indicated through the research that the results of Euler beam model and Timoshenko beam model have great difference for the pile in viscoelastic soil.The fractional derivative order has influence on the peaks of curves of dynamic impedance versus frequency.The dynamic impedance of pile increases with the decrease of constitutive model parameters of the soil.The shear shape factor of pile has great effect on the dynamic impedance.
The lateral vibration equations of the soil described by fractional derivative viscoelastic model are established.The lateral dynamic equivalent stiffness and damping of viscoelastic soil described by fractional derivative viscoelastic model are obtained on the basis of assumed surface strain of Novak.The dynamic interaction between pile and soil is described by equivalent Winkler dynamic spring-damping model,and the pile is simplified as Timoshenko model.The formula of lateral vibration of single pile is established by considering bending and shear deformation.The lateral dynamic impedance of single pile in soil is obtained by considering shear deformation.The influences of fractional derivative order,soil constitutive model parameters and shear shape factor of pile on lateral dynamic impedance are then investigated.It is indicated through the research that the results of Euler beam model and Timoshenko beam model have great difference for the pile in viscoelastic soil.The fractional derivative order has influence on the peaks of curves of dynamic impedance versus frequency.The dynamic impedance of pile increases with the decrease of constitutive model parameters of the soil.The shear shape factor of pile has great effect on the dynamic impedance.
引文
[1]Novak M.Dynamic stiffness and damping of piles[J].Canadian Geotechnical Journal1,9741,1:574-598.
[2]Novak M,Nogami T.Soil-pile interaction in horizontal vibration[J].Earthquake Engineering and Structural Dynamics,1977,5:263-281
[3]Nogami T,Novak M.Resistance of soil to a horizontally vibrating pile[J].Earthquake Engineering and Structural Dynamics,1977,5:247-261.
[4]胡安峰,谢康和,应宏伟,等.粘弹性地基中考虑桩体剪切变形的单桩水平振动解析理论[J].岩石力学与工程学报,2004,23(9):1515-1520.
[5]胡安峰,谢康和.双层地基中考虑桩体剪切变形的单桩水平振动解析解[J].岩石力学与工程学报,2004,23(13):2298-2304.
[6]周绪红,蒋建国,皱银生.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2,0053,8(2):87-91.
[7]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.
[8]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.
[9]刘林超,杨骁.竖向集中力作用下分数导数型半无限体粘弹性地基变形分析[J].工程力学,2009,26(1):13-17.
[10]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.
[11]孙海忠,张卫.一种分析软土黏弹性的分数导数开尔文模型[J].岩土力学2,0072,8(9):1983-1986.
[12]Timoshenko S P.Theory of elasticity[M].New York:McGraw-Hill Book1,934.
[13]Miller K S,Ross B.An introduction to the fractional calculus and fractional differential equations[M].New York:Wiley1,993.第36卷第3期2011年6月昆明理工大学学报(自然科学版)Journal of Kunming University of Science and Technology(Natural Science Edition)Vol.36 No.3Jun.2011
[2]Novak M,Nogami T.Soil-pile interaction in horizontal vibration[J].Earthquake Engineering and Structural Dynamics,1977,5:263-281
[3]Nogami T,Novak M.Resistance of soil to a horizontally vibrating pile[J].Earthquake Engineering and Structural Dynamics,1977,5:247-261.
[4]胡安峰,谢康和,应宏伟,等.粘弹性地基中考虑桩体剪切变形的单桩水平振动解析理论[J].岩石力学与工程学报,2004,23(9):1515-1520.
[5]胡安峰,谢康和.双层地基中考虑桩体剪切变形的单桩水平振动解析解[J].岩石力学与工程学报,2004,23(13):2298-2304.
[6]周绪红,蒋建国,皱银生.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2,0053,8(2):87-91.
[7]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.
[8]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.
[9]刘林超,杨骁.竖向集中力作用下分数导数型半无限体粘弹性地基变形分析[J].工程力学,2009,26(1):13-17.
[10]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.
[11]孙海忠,张卫.一种分析软土黏弹性的分数导数开尔文模型[J].岩土力学2,0072,8(9):1983-1986.
[12]Timoshenko S P.Theory of elasticity[M].New York:McGraw-Hill Book1,934.
[13]Miller K S,Ross B.An introduction to the fractional calculus and fractional differential equations[M].New York:Wiley1,993.第36卷第3期2011年6月昆明理工大学学报(自然科学版)Journal of Kunming University of Science and Technology(Natural Science Edition)Vol.36 No.3Jun.2011
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