端承粘弹性桩纵向振动的轴对称解析解
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摘要
将桩和土体视为粘弹性介质,在频率域求得了桩轴对称纵向振动时动力响应的解析解,进而得到桩头复刚度的解析表达式.通过数值计算,给出了桩头动刚度因子和等效阻尼随激励频率的响应,考察了土层粘性、桩长径比、桩土模量比、桩泊松比和粘性等参数对桩头刚度因子和等效阻尼的影响.研究表明:由于考虑了桩的径向变形效应以及土层对桩的径向力作用,轴对称解析解的桩头动刚度因子和等效阻尼与经典Euler杆模型桩的桩头动刚度因子和阻尼有较大区别.因此,经典Euler杆模型桩的适用范围具有一定的局限性,在若干情形下应采用基于三维粘弹性的桩纵向振动轴对称模型进行分析.
Regarding the pile and the soil layer as viscoelastic media,the axisymmetric analytical solution for the vertical vibration of the end-bearing pile is obtained in the frequency domain,and the analytical expression for the dynamical complex stiffness of the pile top is presented.Responses of dynamic stiffness factor and equivalent damping of the pile top to the frequency are shown in figures by means of the numerical method.The influences of the soil's viscosity,slenderness ratio of pile,modulus ratio of the pile to soil,pile's Poisson ratio and viscosity on the stiffness factor and equivalent damping are examined.It is revealed that,due to the effect of the transversal deformation of the pile and the radial force of the soil acting on the pile,the dynamic stiffness factor and equivalent damping derived from the axisymmetrical solution are greatly different from those derived from the classic Euler rod model.Therefore,there are some limitations for the applicability of the Euler rod model for analysis of the vertical vibration of the pile,and the axisymmetric model based on the three dimensional viscoelasticity should be employed under some special cases.
Regarding the pile and the soil layer as viscoelastic media,the axisymmetric analytical solution for the vertical vibration of the end-bearing pile is obtained in the frequency domain,and the analytical expression for the dynamical complex stiffness of the pile top is presented.Responses of dynamic stiffness factor and equivalent damping of the pile top to the frequency are shown in figures by means of the numerical method.The influences of the soil's viscosity,slenderness ratio of pile,modulus ratio of the pile to soil,pile's Poisson ratio and viscosity on the stiffness factor and equivalent damping are examined.It is revealed that,due to the effect of the transversal deformation of the pile and the radial force of the soil acting on the pile,the dynamic stiffness factor and equivalent damping derived from the axisymmetrical solution are greatly different from those derived from the classic Euler rod model.Therefore,there are some limitations for the applicability of the Euler rod model for analysis of the vertical vibration of the pile,and the axisymmetric model based on the three dimensional viscoelasticity should be employed under some special cases.
引文
[1]Poulos H G,Davis E H.Pile Foundation Analysis and Design[M].New York:John Wiley&Sons,1980.
[2]Carlos P F,Marta B R.A further study about the be-haviour of foundation piles and beams in a Winkler-Pasternak soil[J].International Journal of Mechanical Science,2002,44(1):21-36.
[3]Jiang J G,Zhou X H,Zhang J S.Dynamic interaction factor considering axial load[J].Geotechnical and Ge-ological Engineering,2007,25(4):423-429.
[4]Yusuf Yesilce,Hikmet H Catal.Free vibration of piles embedded in soil having different modulus of subgrade reaction[J].Applied Mathematical Model-ling,2008,32(5):889-900.
[5]Novak M.Dynamic stiffness and damping of pile[J].Canadian Geotechnical Journal,1974,11(4):574-598.
[6]Nogami T,Novak M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering&Structural Dynamics,1976,4(3):277-293.
[7]Novak,M.Piles Under Dynamic Loads[C]//Pro-ceedings of the2nd International Conference on Re-cent Advances in Geotechnical Earthquake Engineer-ing and Soil Dynamics,Vol.3,Rolla,Missouri:Uni-versity of Missouri-Rolla,1991:2433-2456.
[8]胡昌斌,王奎华,谢康和.桩与粘性阻尼土耦合纵向振动时桩顶时域响应研究[J].振动工程学报,2004,17(1):72-77.(Hu C B,Wang K H,Xie K H.Time do-main axial response of dynamically loaded pile in vis-cous damping soil layer[J].Journal of Vibration Engi-neering,2004,17(1):72-77.(in Chinese))
[9]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 C B,Huang X M.A quasi-analyti-cal solution to soil-pile interaction in longitudinal vi-bration in layered soils considering vertical wave effect on soils[J].Earthquake Engineering and Engi-neering Vibration,2006,26(4):205-211.(in Chi-nese))
[10]Zeng X,Rajapakse R K N D.Dynamic axial load transfer from elastic bar to poroelastic medium[J].ASCE Journal of Engineering Mechanics,1999,125(9):1048-1055.
[11]李强,王奎华,谢康和.饱和土中大直径嵌岩桩纵向振动特性研究[J].振动工程学报,2005,18(4):500-505.(Li Q,Wang K H,Xie K H.Dynamic response for vertical vibration of large diameter pile in saturat-ed soil[J].Journal of Vibration Engineering,2005,18(4):500-505.(in Chinese))
[12]杨骁,蔡雪琼.考虑横向惯性效应的饱和粘弹性土层中端承桩的纵向振动[J].岩土力学,2011,32(6):1857-1863.(Yang X,Cai X Q.Vertical vibration of pile in saturated viscoelastic soil layer with transver-sal effects[J].Rock and Soil Mechanics,2011,32(6):1857-1863.(in Chinese))
[13]Yang X,Pan Y.Axisymmetrical analytical solution for vertical vibration of end-bearing pile in saturated vis-coelastic soil layer[J].Journal of Applied Mathemat-ics and Mechanics,2010,31(2),193-204.
[14]Christensen R M.Theory of Viscoelasticity,an Intro-duction[M].2nd ed.New York:Academic Press Inc,1982:1-33.
[15]Chau K T,Yang X.Nonlinear interaction of soil-pile in horizontal vibration[J].Journal of Engineering Me-chanics,2005,131(8):847-858.
[2]Carlos P F,Marta B R.A further study about the be-haviour of foundation piles and beams in a Winkler-Pasternak soil[J].International Journal of Mechanical Science,2002,44(1):21-36.
[3]Jiang J G,Zhou X H,Zhang J S.Dynamic interaction factor considering axial load[J].Geotechnical and Ge-ological Engineering,2007,25(4):423-429.
[4]Yusuf Yesilce,Hikmet H Catal.Free vibration of piles embedded in soil having different modulus of subgrade reaction[J].Applied Mathematical Model-ling,2008,32(5):889-900.
[5]Novak M.Dynamic stiffness and damping of pile[J].Canadian Geotechnical Journal,1974,11(4):574-598.
[6]Nogami T,Novak M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering&Structural Dynamics,1976,4(3):277-293.
[7]Novak,M.Piles Under Dynamic Loads[C]//Pro-ceedings of the2nd International Conference on Re-cent Advances in Geotechnical Earthquake Engineer-ing and Soil Dynamics,Vol.3,Rolla,Missouri:Uni-versity of Missouri-Rolla,1991:2433-2456.
[8]胡昌斌,王奎华,谢康和.桩与粘性阻尼土耦合纵向振动时桩顶时域响应研究[J].振动工程学报,2004,17(1):72-77.(Hu C B,Wang K H,Xie K H.Time do-main axial response of dynamically loaded pile in vis-cous damping soil layer[J].Journal of Vibration Engi-neering,2004,17(1):72-77.(in Chinese))
[9]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 C B,Huang X M.A quasi-analyti-cal solution to soil-pile interaction in longitudinal vi-bration in layered soils considering vertical wave effect on soils[J].Earthquake Engineering and Engi-neering Vibration,2006,26(4):205-211.(in Chi-nese))
[10]Zeng X,Rajapakse R K N D.Dynamic axial load transfer from elastic bar to poroelastic medium[J].ASCE Journal of Engineering Mechanics,1999,125(9):1048-1055.
[11]李强,王奎华,谢康和.饱和土中大直径嵌岩桩纵向振动特性研究[J].振动工程学报,2005,18(4):500-505.(Li Q,Wang K H,Xie K H.Dynamic response for vertical vibration of large diameter pile in saturat-ed soil[J].Journal of Vibration Engineering,2005,18(4):500-505.(in Chinese))
[12]杨骁,蔡雪琼.考虑横向惯性效应的饱和粘弹性土层中端承桩的纵向振动[J].岩土力学,2011,32(6):1857-1863.(Yang X,Cai X Q.Vertical vibration of pile in saturated viscoelastic soil layer with transver-sal effects[J].Rock and Soil Mechanics,2011,32(6):1857-1863.(in Chinese))
[13]Yang X,Pan Y.Axisymmetrical analytical solution for vertical vibration of end-bearing pile in saturated vis-coelastic soil layer[J].Journal of Applied Mathemat-ics and Mechanics,2010,31(2),193-204.
[14]Christensen R M.Theory of Viscoelasticity,an Intro-duction[M].2nd ed.New York:Academic Press Inc,1982:1-33.
[15]Chau K T,Yang X.Nonlinear interaction of soil-pile in horizontal vibration[J].Journal of Engineering Me-chanics,2005,131(8):847-858.
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