轴对称径向非均质土中单桩纵向振动特性研究
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摘要
为了分析径向非均质土中单桩纵向振动特性,基于复刚度传递径向多圈层并采用黏性阻尼模型描述桩周土材料阻尼,建立了三维轴对称径向成层非均质土体中桩基纵向振动简化分析模型。采用Laplace变换和复刚度传递方法,递推得出桩周土体与桩体界面处复刚度,进而利用桩-土完全耦合条件推导得出桩顶动力阻抗解析解,并将所得解退化到均质土情况,与已有解答进行比较验证其合理性。在此基础上对桩基纵向振动特性进行参数化分析,计算结果表明:桩周土体阻尼系数、桩底土阻尼因子仅对桩顶动力阻抗曲线振幅有较明显的影响,而桩底土刚度因子对桩顶动力阻抗曲线振幅及共振频率均有显著影响;桩周土软(硬)化程度越高(低),桩顶动力阻抗曲线振幅越大(小);桩周土软(硬)化范围越大,桩顶动力阻抗曲线振幅水平越高(低);但桩周土软(硬)化程度、软(硬)化范围对桩顶动力阻抗曲线共振频率影响则可忽略。
For the aim to analyze the vibration characteristics of a single pile surrounded by radially inhomogeous soil, a simplified mechanical model for vertical vibration of a single pile embedded in a radially inhomogeneous viscoelastic soil is proposed by employing the viscous damping and three-dimensional axisymmetric continuum model with annular transferred complex stiffness. Firstly, the complex stiffness at the interfaces between soil and pile is derived using Laplace transform and complex stiffness transfer method. Secondly, an analytical solution for dynamic impedance at the pile head is obtained by using the compatibility condition of pile and radially inhomogeneous surrounding soil. Furthermore, the obtained analytical solution for dynamic impedance at the pile head is reduced to verify its validity by comparison with an existing solution. Extensive parametric analyses are performed to investigate the effects of the parameters on the vibration characteristics at pile head. The computational results show that the viscous damping coefficient and the damping factor only have significant influence on the amplitude of dynamic impedance at pile head, while the stiffness factor has significant influence on the amplitude and resonance frequency of dynamic impedance at pile head. The higher the degree of softening(hardening) of the surrounding soil, the larger(smaller) the amplitude of the dynamic impedance at pile head. The larger the range of softening(hardening) of the soil around the pile, the higher(lower) the level of the dynamic impedance at pile head. However, the influences of the degree of softening(hardening) of the soil around the pile and the range of softening(hardening) on the resonance frequency of the dynamic impedance at pile head can be neglected.
For the aim to analyze the vibration characteristics of a single pile surrounded by radially inhomogeous soil, a simplified mechanical model for vertical vibration of a single pile embedded in a radially inhomogeneous viscoelastic soil is proposed by employing the viscous damping and three-dimensional axisymmetric continuum model with annular transferred complex stiffness. Firstly, the complex stiffness at the interfaces between soil and pile is derived using Laplace transform and complex stiffness transfer method. Secondly, an analytical solution for dynamic impedance at the pile head is obtained by using the compatibility condition of pile and radially inhomogeneous surrounding soil. Furthermore, the obtained analytical solution for dynamic impedance at the pile head is reduced to verify its validity by comparison with an existing solution. Extensive parametric analyses are performed to investigate the effects of the parameters on the vibration characteristics at pile head. The computational results show that the viscous damping coefficient and the damping factor only have significant influence on the amplitude of dynamic impedance at pile head, while the stiffness factor has significant influence on the amplitude and resonance frequency of dynamic impedance at pile head. The higher the degree of softening(hardening) of the surrounding soil, the larger(smaller) the amplitude of the dynamic impedance at pile head. The larger the range of softening(hardening) of the soil around the pile, the higher(lower) the level of the dynamic impedance at pile head. However, the influences of the degree of softening(hardening) of the soil around the pile and the range of softening(hardening) on the resonance frequency of the dynamic impedance at pile head can be neglected.
引文
[1]崔春义,张石平,杨刚,等.考虑桩底土层波动效应的饱和黏弹性半空间中摩擦桩竖向振动[J].岩土工程学报,2015,37(5):878-892.CUI Chun-yi,ZHANG Shi-ping,YANG Gang,et al.Vertical vibration of floating piles in saturated viscoelastic half-space considering wave effect of subsoil under pile bottom[J].Chinese Journal of Geotechnical Engineering,2015,37(5):878-892.
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[15]EI NAGGAR M H,NOVAK M.Nonlinear axial interaction in pile dynamics[J].Journal of Geotechnical Engineering,1994,120(4):678-696.
[16]EI NAGGAR M H.Vertical and torsional soil reactions for radially inhomogeneous soil layer[J].Structural Engineering&Mechanics,2000,10(4):299-312.
[17]王奎华,杨冬英,张智卿,等.基于复刚度传递多圈层平面应变模型的桩动力响应研究[J].岩石力学与工程学报,2008,27(4):825-831.WANG Kui-hua,YANG Dong-ying,ZHANG Zhi-qing,et al.Study on dynamic response of pile based on complex stiffness transfer model of radial multizone plane strain[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(4):825-831.
[18]杨冬英,王奎华.任意圈层径向非均质土中桩的纵向振动特性[J].力学学报,2009,41(2):243-252.YANG Dong-ying,WANG Kui-hua.Vertical vibration of pile in radially inhomogeneous soil layers[J].Chinese Journal of Theoretical&Applied Mechanics,2009,41(2):243-252.
[19]WANG K H,YANG D Y,ZHANG Z Q,et al.A new approach for vertical impedance in radially inhomogeneous soil layer[J].International Journal for Numerical&Analytical Methods in Geomechanics,2012,36(6):697-707.
[20]王奎华,杨冬英,张智卿.两种径向多圈层土体平面应变模型的对比[J].浙江大学学报(工学版),2009,43(10):1902-1908.WANG Kui-hua,YANG Dong-ying,ZHANG Zhi-qing.Comparison on two kinds of radial multi-zone plane strain models[J].Journal of Zhejiang University(Engineering Science),2009,43(10):1902-1908.
[21]杨冬英,王奎华,丁海平.三维非均质土中黏弹性桩-土纵向耦合振动响应[J].土木建筑与环境工程,2011,33(3):80-87.YANG Dong-ying,WANG Kui-hua,DING Hai-ping.Axial response of viscoelastic pile-soil coupling interaction in three-dimensional inhomogeneous soil[J].Journal of Civil Architectural&Environmental Engineering,2011,33(3):80-87.
[22]YANG D Y,WANG K H,ZHANG Z Q,et al.Vertical dynamic response of pile in a radially heterogeneous soil layer[J].International Journal for Numerical&Analytical Methods in Geomechanics,2009,33(8):1039-1054.
[23]杨冬英,王奎华,丁海平.双向非均质土中基于连续介质模型的桩动力响应特性分析[J].土木工程学报,2013,46(3):119-126.YANG Dong-ying,WANG Kui-hua,DING Hai-ping.Vertical vibration of pile based on continuum medium model in vertically and radially inhomogeneous soil layers[J].China Civil Engineering Journal,2013,46(3):119-126.
[24]胡昌斌,王奎华,谢康和.桩与黏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 Chang-bin,WANG Kui-hua,XIE Kang-he.Time domain axial response of dynamically loaded pile in viscous damping soil layer[J].Journal of Vibration Engineering,2004,17(1):72-77.
[25]NOGAMI T,NOVAK M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering&Structural Dynamics,1976,4(3):277-293.
[26]MILITANO G,RAJAPAKSE R K N D.Dynamic response of a pile in a multi-layered soil transient torsional and axial loading[J].Géotechnique,1999,49(1):91-109.
[27]胡海岩.结构阻尼模型及系统时域动响应[J].应用力学学报,1993,(1):8-16.HU Hai-yan.Structural damping model and system dynamic response at time domain[J].Chinese Journal of Applied Mechanics,1993,(1):8-16.
[28]廖振鹏.工程波动理论导论[M].北京:科学出版社,2002.LIAO Zhen-peng.Introduction to engineering wave theory[M].Beijing:Science Press,2002.
[2]CUI Chun-yi,ZHANG Shi-ping,YANG Gang,et al.Vertical vibration of a floating pile in a saturated viscoelastic soil layer overlaying bedrock[J].Journal of Central South University,2016,23(1):220-232.
[3]HAN Y,VAZIRI H.Dynamic response of pile groups under lateral loading[J].Soil Dynamics&Earthquake Engineering,1992,11(2):87-99.
[4]WU W B,JIANG G S,DOU B,et al.Vertical dynamic impedance of tapered pile considering compacting effect[J].Mathematical Problems in Engineering,2013,(2):1-9.
[5]NOVAK M,SHETA M.Approximate approach to contact problems of piles[C]//Proceedings of the Geotechnical Engineering Division.Florida:American Society of Civil Engineering National Convention,1980:53-79.
[6]NOVAK M,HAN Y C.Impedances of soil layer with boundary zone[J].Journal of Geotechnical Engineering,1990,116(6):1008-1014.
[7]VELETSOS A S,DOTSON K W.Impedances of soil layer with disturbed boundary zone[J].Journal of Geotechnical Engineering,1986,112(3):363-368.
[8]VELETSOS A S,DOTSON K W.Vertical and torsional vibration of foundations in inhomogeneous media[J].Journal of Geotechnical Engineering,1988,114(9):1002-1021.
[9]NOGAMI T,KONAGAI K.Dynamic response of vertically loaded nonlinear pile foundations[J].Journal of Geotechnical Engineering,1987,113(2):147-160.
[10]NOGAMI T,KONAGAI K.Time domain flexural response of dynamically loaded single piles[J].Journal Engineering Mechanics,ASCE,1988,114(9):1512-1525.
[11]DOTSON K W,VELETSOS A S.Vertical and torsional impedances for radially inhomogeneous viscoelastic soil layers[J].Soil Dynamics&Earthquake Engineering,1990,9(3):110-119.
[12]VAZIRI H,HAN Y.Impedance functions of piles in inhomogeneous media[J].Journal of Geotechnical Engineering,1993,119(9):1414-1430.
[13]HAN Y C,SABIN G C W.Impedances for radially inhomogeneous viscoelastic soil media[J].Journal of Engineering Mechanics,1995,121(9):939-947.
[14]HAN Y C.Dynamic vertical response of piles in nonlinear soil[J].Journal of Geotechnical&Geoenvironmental Engineering,1997,123(8):710-716.
[15]EI NAGGAR M H,NOVAK M.Nonlinear axial interaction in pile dynamics[J].Journal of Geotechnical Engineering,1994,120(4):678-696.
[16]EI NAGGAR M H.Vertical and torsional soil reactions for radially inhomogeneous soil layer[J].Structural Engineering&Mechanics,2000,10(4):299-312.
[17]王奎华,杨冬英,张智卿,等.基于复刚度传递多圈层平面应变模型的桩动力响应研究[J].岩石力学与工程学报,2008,27(4):825-831.WANG Kui-hua,YANG Dong-ying,ZHANG Zhi-qing,et al.Study on dynamic response of pile based on complex stiffness transfer model of radial multizone plane strain[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(4):825-831.
[18]杨冬英,王奎华.任意圈层径向非均质土中桩的纵向振动特性[J].力学学报,2009,41(2):243-252.YANG Dong-ying,WANG Kui-hua.Vertical vibration of pile in radially inhomogeneous soil layers[J].Chinese Journal of Theoretical&Applied Mechanics,2009,41(2):243-252.
[19]WANG K H,YANG D Y,ZHANG Z Q,et al.A new approach for vertical impedance in radially inhomogeneous soil layer[J].International Journal for Numerical&Analytical Methods in Geomechanics,2012,36(6):697-707.
[20]王奎华,杨冬英,张智卿.两种径向多圈层土体平面应变模型的对比[J].浙江大学学报(工学版),2009,43(10):1902-1908.WANG Kui-hua,YANG Dong-ying,ZHANG Zhi-qing.Comparison on two kinds of radial multi-zone plane strain models[J].Journal of Zhejiang University(Engineering Science),2009,43(10):1902-1908.
[21]杨冬英,王奎华,丁海平.三维非均质土中黏弹性桩-土纵向耦合振动响应[J].土木建筑与环境工程,2011,33(3):80-87.YANG Dong-ying,WANG Kui-hua,DING Hai-ping.Axial response of viscoelastic pile-soil coupling interaction in three-dimensional inhomogeneous soil[J].Journal of Civil Architectural&Environmental Engineering,2011,33(3):80-87.
[22]YANG D Y,WANG K H,ZHANG Z Q,et al.Vertical dynamic response of pile in a radially heterogeneous soil layer[J].International Journal for Numerical&Analytical Methods in Geomechanics,2009,33(8):1039-1054.
[23]杨冬英,王奎华,丁海平.双向非均质土中基于连续介质模型的桩动力响应特性分析[J].土木工程学报,2013,46(3):119-126.YANG Dong-ying,WANG Kui-hua,DING Hai-ping.Vertical vibration of pile based on continuum medium model in vertically and radially inhomogeneous soil layers[J].China Civil Engineering Journal,2013,46(3):119-126.
[24]胡昌斌,王奎华,谢康和.桩与黏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 Chang-bin,WANG Kui-hua,XIE Kang-he.Time domain axial response of dynamically loaded pile in viscous damping soil layer[J].Journal of Vibration Engineering,2004,17(1):72-77.
[25]NOGAMI T,NOVAK M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering&Structural Dynamics,1976,4(3):277-293.
[26]MILITANO G,RAJAPAKSE R K N D.Dynamic response of a pile in a multi-layered soil transient torsional and axial loading[J].Géotechnique,1999,49(1):91-109.
[27]胡海岩.结构阻尼模型及系统时域动响应[J].应用力学学报,1993,(1):8-16.HU Hai-yan.Structural damping model and system dynamic response at time domain[J].Chinese Journal of Applied Mechanics,1993,(1):8-16.
[28]廖振鹏.工程波动理论导论[M].北京:科学出版社,2002.LIAO Zhen-peng.Introduction to engineering wave theory[M].Beijing:Science Press,2002.