三维轴对称条件下基于虚土桩法的单桩纵向振动分析
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摘要
虚土桩法是一种处理桩底支撑的新方法,该方法将桩体正下方投影到基岩的土体简化为虚土桩,求解时将其看作桩体。以桩轴心线为Z轴,建立轴对称坐标体系,通过虚土桩与土体的边界条件,求解得到虚土桩桩顶的复刚度。将该复刚度作为实体桩桩底的支撑刚度,结合实体桩与土体的边界条件,利用复阻抗传递法得到单桩桩顶的复刚度和速度响应函数。通过数值计算,分析了桩底土体的虚土桩长度、剪切波速及泊松比等参数对单桩动力响应的影响;对比了虚土桩法与其他不同桩底支承的异同,进一步评价了虚土桩法的优越性和合理性;结果表明,虚土桩法可以模拟弹(黏)性支撑和固定支撑,是一种较为严格的计算模型,具有进一步研究的价值。
A new treatment way for the supporting soil under physical piles,the fictitious soil pile method,is introduced,in which the projection zone of the soil from immediately below the physical pile till the bedrock is simplified as a fictitious soil pile.A three-dimensional axisymmetric coordination is established with the axial line of pile as the Z axis.Firstly the complex stiffness of the fictitious pileblock is obtained by solving the vibration equation with its boundary condition.Further,regarding the complex stiffness of the fictitious pileblock as the supporting stiffness of physical pile,both complex stiffness and velocity response function of the physical pilebolck are obtained using the complex impedance transfer method based on the boundary condition of the physical pile.Effects of length,velocity of shear wave and Poisson ratio of the fictitious soil pile on dynamic responses of the physical pile are also investigated.Finally,compared to some other methods for the pile supporting,the advantages and rationality of the fictitious soil pile method are identified.It is indicated that the fictitious soil pile method is a more precise computational modeling for simulating elastic(viscous) and fixed supporting,and is worth further studing.
A new treatment way for the supporting soil under physical piles,the fictitious soil pile method,is introduced,in which the projection zone of the soil from immediately below the physical pile till the bedrock is simplified as a fictitious soil pile.A three-dimensional axisymmetric coordination is established with the axial line of pile as the Z axis.Firstly the complex stiffness of the fictitious pileblock is obtained by solving the vibration equation with its boundary condition.Further,regarding the complex stiffness of the fictitious pileblock as the supporting stiffness of physical pile,both complex stiffness and velocity response function of the physical pilebolck are obtained using the complex impedance transfer method based on the boundary condition of the physical pile.Effects of length,velocity of shear wave and Poisson ratio of the fictitious soil pile on dynamic responses of the physical pile are also investigated.Finally,compared to some other methods for the pile supporting,the advantages and rationality of the fictitious soil pile method are identified.It is indicated that the fictitious soil pile method is a more precise computational modeling for simulating elastic(viscous) and fixed supporting,and is worth further studing.
引文
[1]NOGAMI T,KONAGAI K.Time domain axial response of dynamically loaded single piles[J].Journal of Engineering Mechanics,ASCE,1986,112(11):1241-1252.
[2]NOGAMI T,KONAGAI K.Dynamic response of vertically loaded nonlinear pile foundations[J].Journal of Geotechnical Engineering,ASCE,1987,113(2):147-160.
[3]WANG T,WANG K H,XIE K H.An analytical solution to longitudinal vibration of a pile of arbitrary segments with variable modulus[J].Acta Mechanica Solida Sinica,2001,14(1):67-73.
[4]孔德森,栾茂田,杨庆.桩土相互作用分析中的动态Winkler模型研究评述[J].世界地震工程,2005,21(1):12-17.(KONG De-sen,LUAN Mao-tian,YANG Qing.Review of dynamic Winkler model appfied in pile-soil interaction analyses[J].World Earthquake Engineering,2005,21(1):12-17.(in Chinese))
[5]NOGAMI T,NOVAK M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering and Structural Dynamics,1976,4:277-293.
[6]HAN Y C.Dynamic vertical response of piles in nonlinear soil[J].Journal of Geotechnical and Geoenvironmental Engineering,ASCE,1997,123(8):710-716.
[7]ELNAGGAR MH.Vertical and torsional soil reactions for radially inhomogeneous soil layer[J].Structural Engineering and Mechanics,2000,10(4):299-312.
[8]NOGAMI T,HARN S C.Dynamic soil stiffnesses at side of embedded structures with rectangular base[J].Journal of Engineering Mechanics,ASCE,2003,129(8):963-973.
[9]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 Chang-bin,WANG Kui-hua,XIE Kang-he.Soil-pile interaction in vertical vibrations of a pile with elastic bottom boundaries and its application[J].Engineering Mechanics,2003,20(2):146-154.(in Chinese))
[10]王奎华,阙仁波,夏建中.考虑土体真三维波动效应时桩的振动理论及对近似理论的校核[J].岩石力学与工程学报,2005,24(8):1362-1370.(WANG Kui-hua,QUE Ren-bo,XIA Jian-zhong.Theory of pile vibration considering true three-dimensional wave effect of soil and its check on the approximate theories[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(8):1362-1370.(in Chinese))
[11]LYSMER J,RICHART FE.Dynamic response of footing to vertical load[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1966,2(1):65-91.
[12]NOVAK M,BEREDUGO YO.Vertical vibration of embedded footings[J].Journal of Mechanics and Foundation Division,ASCE.1972,98(SM12):1291-1310.
[13]LIANG R Y,HUSEIN A I.Simplified dynamic method for pile-driving control[J].Journal of Geotechnical and Geoenvironmental Engineering,ASCE,1993,119(4):694-713.
[14]MEYERHOLF G G.Bearing capacity and settlement of pile foundations[J].Journal of Geotechnical Engineering Division,ASCE,1976,102(GT3):195-228.
[15]陈嘉熙.虚土桩法可行性初步研究与分析[D].杭州:浙江大学,2008.(CHEN Jia-xi.Preliminary feasibility studies and analysis on method of virtual pile of soil[D].Hangzhou:Zhejiang University,2008.(in Chinese))
[16]杨冬英.复杂非均质土中竖向振动理论研究[D].杭州:浙江大学,2009.(YANG Dong-ying.Study on pile vertical vibration in inhomogeneous soil[D].Hangzhou:Zhejiang University,2009.(in Chinese))
[17]SENJUNTICHAIA T,MANIA S,RAJAPAKSEB R K N D.Vertical vibration of an embedded rigid foundation in a poroelastic soil[J].Soil Dynamics and Earthquake Engineering,2006,26:626-636.
[2]NOGAMI T,KONAGAI K.Dynamic response of vertically loaded nonlinear pile foundations[J].Journal of Geotechnical Engineering,ASCE,1987,113(2):147-160.
[3]WANG T,WANG K H,XIE K H.An analytical solution to longitudinal vibration of a pile of arbitrary segments with variable modulus[J].Acta Mechanica Solida Sinica,2001,14(1):67-73.
[4]孔德森,栾茂田,杨庆.桩土相互作用分析中的动态Winkler模型研究评述[J].世界地震工程,2005,21(1):12-17.(KONG De-sen,LUAN Mao-tian,YANG Qing.Review of dynamic Winkler model appfied in pile-soil interaction analyses[J].World Earthquake Engineering,2005,21(1):12-17.(in Chinese))
[5]NOGAMI T,NOVAK M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering and Structural Dynamics,1976,4:277-293.
[6]HAN Y C.Dynamic vertical response of piles in nonlinear soil[J].Journal of Geotechnical and Geoenvironmental Engineering,ASCE,1997,123(8):710-716.
[7]ELNAGGAR MH.Vertical and torsional soil reactions for radially inhomogeneous soil layer[J].Structural Engineering and Mechanics,2000,10(4):299-312.
[8]NOGAMI T,HARN S C.Dynamic soil stiffnesses at side of embedded structures with rectangular base[J].Journal of Engineering Mechanics,ASCE,2003,129(8):963-973.
[9]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 Chang-bin,WANG Kui-hua,XIE Kang-he.Soil-pile interaction in vertical vibrations of a pile with elastic bottom boundaries and its application[J].Engineering Mechanics,2003,20(2):146-154.(in Chinese))
[10]王奎华,阙仁波,夏建中.考虑土体真三维波动效应时桩的振动理论及对近似理论的校核[J].岩石力学与工程学报,2005,24(8):1362-1370.(WANG Kui-hua,QUE Ren-bo,XIA Jian-zhong.Theory of pile vibration considering true three-dimensional wave effect of soil and its check on the approximate theories[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(8):1362-1370.(in Chinese))
[11]LYSMER J,RICHART FE.Dynamic response of footing to vertical load[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1966,2(1):65-91.
[12]NOVAK M,BEREDUGO YO.Vertical vibration of embedded footings[J].Journal of Mechanics and Foundation Division,ASCE.1972,98(SM12):1291-1310.
[13]LIANG R Y,HUSEIN A I.Simplified dynamic method for pile-driving control[J].Journal of Geotechnical and Geoenvironmental Engineering,ASCE,1993,119(4):694-713.
[14]MEYERHOLF G G.Bearing capacity and settlement of pile foundations[J].Journal of Geotechnical Engineering Division,ASCE,1976,102(GT3):195-228.
[15]陈嘉熙.虚土桩法可行性初步研究与分析[D].杭州:浙江大学,2008.(CHEN Jia-xi.Preliminary feasibility studies and analysis on method of virtual pile of soil[D].Hangzhou:Zhejiang University,2008.(in Chinese))
[16]杨冬英.复杂非均质土中竖向振动理论研究[D].杭州:浙江大学,2009.(YANG Dong-ying.Study on pile vertical vibration in inhomogeneous soil[D].Hangzhou:Zhejiang University,2009.(in Chinese))
[17]SENJUNTICHAIA T,MANIA S,RAJAPAKSEB R K N D.Vertical vibration of an embedded rigid foundation in a poroelastic soil[J].Soil Dynamics and Earthquake Engineering,2006,26:626-636.
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