饱和土中摩擦桩竖向振动解析解及应用
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摘要
采用与频率相关的桩土接触面模型建立了三维轴对称条件下摩擦桩在饱和土中的竖向耦合振动模型,通过势函数分解法和分离变量法求解了饱和土动力固结方程,利用桩土耦合条件得到摩擦桩竖向振动解,对桩周剪应力分布、桩顶的频率和时域响应进行了参数研究。结果表明,桩底支承系数和桩土接触面动刚度对桩土荷载传递有明显影响,频率相关的阻尼系数可以有效地抑制桩顶速度幅频的高频发散现象。最后通过与基桩实测结果对比,表明该模型可以较好地与基桩完整性测试结果吻合。
A dynamic model of a friction pile embedded in saturated soil is established on the basis of interface model with a frequent-dependent damping between the pile and the soil.With the use of potential functions and a variable separation method,the pile dynamic response to an arbitrary vertical load is analytically derived in a closed form under the assumption of the imperfect contact between the pile and soil and an elastic bearing at the pile toe.Furthermore,a parametric study is conducted to find out the main features of the soil-pile interaction,as a result,the bearing stiffness at pile toe and soil stiffness of the pile shaft have major effects on dynamic load transfer at the contact surface of the pile and soil.And frequent dependent damping of the contact surface can restrain high frequency divergence effectively.Finally,it is shown that the theoretical curves of the present solution are in good agreement with those obtained from pile integrity test.
A dynamic model of a friction pile embedded in saturated soil is established on the basis of interface model with a frequent-dependent damping between the pile and the soil.With the use of potential functions and a variable separation method,the pile dynamic response to an arbitrary vertical load is analytically derived in a closed form under the assumption of the imperfect contact between the pile and soil and an elastic bearing at the pile toe.Furthermore,a parametric study is conducted to find out the main features of the soil-pile interaction,as a result,the bearing stiffness at pile toe and soil stiffness of the pile shaft have major effects on dynamic load transfer at the contact surface of the pile and soil.And frequent dependent damping of the contact surface can restrain high frequency divergence effectively.Finally,it is shown that the theoretical curves of the present solution are in good agreement with those obtained from pile integrity test.
引文
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[3]Zhou Xianglian,Wang Jianhua,Jiang Lingfa.Transient dynamic response of pile to vertical load in saturated soil[J].Mechanics Research Communications,2009,36:618―624.
[4]Nogami T,Novak M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering and Structural Dynamics,1976,4:277―293.
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[6]阙仁波,王奎华.考虑土体三维波动效应时弹性支承桩的振动理论及其应用[J].计算力学学报,2005,22(6):658―665.Que Renbo,Wang Kuihua.Theory of vibration of pile on elastic foundation considering3D wave effect of soil and its applications[J].Chinese Journal of Computational Mechanics,2005,22(6):658―665.(in Chinese)
[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 Qiang,Wang Kuihua,Xie Kanghe.Vertical vibration of an end bearing pile embedded in saturated soil[J].Acta Mech Sinica,2004,36(4):435―442.(in Chinese)
[8]李强.饱和土中端承桩非完全粘结下的竖向振动特性[J].水利学报,2007,38(3):349―354.Li Qiang.Vertical vibration of piles embedded in saturated soil considering the imperfect contact[J].Journal of Hydraulic Engineering,2007,38(3):349―354.(in Chinese)
[9]Meymand P J.Shaking table scale model tests of nonlinear soil-pile-superstructure interaction in soft clay[D].Berkeley:University of California,1998.
[10]孔德森,栾茂田,杨庆.桩土相互作用分析中的动力Winkler模型研究评述[J].世界地震工程,2005,21(1):12―17.Kong Desen,Luan Maotian,Yang Qing.Review of dynamic Winkler model applied in pile-soil interaction analyses[J].World Earthquake Engineering,2005,21(1):12―17.(in Chinese)
[11]栾茂田,孔德森.单桩竖向动力阻抗计算方法及其影响因素分析[J].振动工程学报,2004,17(4):500―505.Luan Maotian,Kong Desen.Simplified computational model and parametric studies of vertical dynamic impendence for single pile[J].Journal of VibrationEngineering,2004,17(4):500―505.(in Chinese)
[12]Lin Meei-Ling,Huang Tsan-Hwei,You Jeng-Chie.The effects of frequency on damping properties of sand[J].Soil Dynamics Earthquake Engng,1996,15:269―278.
[13]Chang DerWen,Roesset J M,Wen ChanHua.A time-domain viscous damping model based on frequency dependent damping ratios[J].Soil Dynamics Earthquake Engng.,2000,19:551―558.
[14]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solidⅠ.low-frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):168―178.
[2]Zeng X,Rajapakse RKND.Dynamic axial load transfer from elastic bar to poroelastic medium[J].Journal of Engineering Mechanics,1999,125(9):1048―1055.
[3]Zhou Xianglian,Wang Jianhua,Jiang Lingfa.Transient dynamic response of pile to vertical load in saturated soil[J].Mechanics Research Communications,2009,36:618―624.
[4]Nogami T,Novak M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering and Structural Dynamics,1976,4:277―293.
[5]胡昌斌,王奎华,谢康和.考虑桩土耦合作用时弹性支承桩纵向振动特性分析及应用[J].工程力学,2003,20(2):146―154.Hu Changbin,Wang Kuihua,Xie Kanghe.Soil-pile interaction in vertical vibrations of a pile with elastic bottom boundaries and its applications[J].Engineering Mechanics,2003,20(2):146―154.(in Chinese)
[6]阙仁波,王奎华.考虑土体三维波动效应时弹性支承桩的振动理论及其应用[J].计算力学学报,2005,22(6):658―665.Que Renbo,Wang Kuihua.Theory of vibration of pile on elastic foundation considering3D wave effect of soil and its applications[J].Chinese Journal of Computational Mechanics,2005,22(6):658―665.(in Chinese)
[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 Qiang,Wang Kuihua,Xie Kanghe.Vertical vibration of an end bearing pile embedded in saturated soil[J].Acta Mech Sinica,2004,36(4):435―442.(in Chinese)
[8]李强.饱和土中端承桩非完全粘结下的竖向振动特性[J].水利学报,2007,38(3):349―354.Li Qiang.Vertical vibration of piles embedded in saturated soil considering the imperfect contact[J].Journal of Hydraulic Engineering,2007,38(3):349―354.(in Chinese)
[9]Meymand P J.Shaking table scale model tests of nonlinear soil-pile-superstructure interaction in soft clay[D].Berkeley:University of California,1998.
[10]孔德森,栾茂田,杨庆.桩土相互作用分析中的动力Winkler模型研究评述[J].世界地震工程,2005,21(1):12―17.Kong Desen,Luan Maotian,Yang Qing.Review of dynamic Winkler model applied in pile-soil interaction analyses[J].World Earthquake Engineering,2005,21(1):12―17.(in Chinese)
[11]栾茂田,孔德森.单桩竖向动力阻抗计算方法及其影响因素分析[J].振动工程学报,2004,17(4):500―505.Luan Maotian,Kong Desen.Simplified computational model and parametric studies of vertical dynamic impendence for single pile[J].Journal of VibrationEngineering,2004,17(4):500―505.(in Chinese)
[12]Lin Meei-Ling,Huang Tsan-Hwei,You Jeng-Chie.The effects of frequency on damping properties of sand[J].Soil Dynamics Earthquake Engng,1996,15:269―278.
[13]Chang DerWen,Roesset J M,Wen ChanHua.A time-domain viscous damping model based on frequency dependent damping ratios[J].Soil Dynamics Earthquake Engng.,2000,19:551―558.
[14]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solidⅠ.low-frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):168―178.
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