三维饱和层状土–虚土桩–实体桩体系纵向振动频域分析
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摘要
为分析饱和土中浮承桩纵向振动特性,基于Biot波动理论提出一种桩底饱和虚土桩模型,并建立三维饱和层状土–虚土桩–实体桩耦合纵向振动体系定解问题。采用势函数法、桩–土耦合条件及阻抗函数传递性求解得出桩顶纵向振动动力阻抗解析解答,并通过多元退化验证所提出解析解的正确性。在此基础上,对浮承桩纵向振动特性影响因素进行参数化分析,结果表明:当桩底土饱和性显著且排水性较差时,桩底土单相虚土桩模型会过低估计阻抗曲线共振频率,宜采用饱和虚土桩模型和所得相关解析解答分析浮承桩纵向振动特性。桩周饱和软(硬)夹层对桩顶动力阻抗曲线振幅水平影响显著,而桩底软(硬)下卧夹层则对桩顶动力阻抗曲线影响很小。桩周饱和表层土体孔隙率仅对桩顶动力阻抗曲线共振幅值产生明显影响,而桩底饱和土层孔隙率对桩顶动力阻抗曲线共振幅值和共振频率均影响显著。
In order to study the longitudinal vibration characteristics of floating piles in saturated soil,a saturated virtual soil pile model based on Biot′s wave theory was proposed,and a coupled longitudinal vibration system of three-dimensional saturated layered soil,virtual soil piles and solid piles was established. The analytical solution of the displacement of saturated soil was derived by potential function method,and the vertical dynamic impedance at the pile head was obtained by using the pile-soil compatibility conditions and the transfer method of impedance function. The validity of the obtained solution was verified by degrading to existing solutions,and parametric analyses were performed to investigate the effects of the parameters of the saturated soil on the vibration characteristics at the pile head. The results show that,when the saturation of soil layers beneath the pile toe is remarkable and the drainage is poor,the saturated virtual soil pile model and the relevant analytical solution is more suitable to analyze the longitudinal vibration characteristics of floating piles. The longitudinal interlayer of surrounding soil has obvious effect on the amplitude of the dynamic impedance at the pile head,but the effect of longitudinal interlayer of soil beneath the pile toe on the dynamic impedance at the pile head can be ignored. The porosity of saturated surface surrounding soil has obvious influence only on the resonance amplitude of the dynamic impedance at the pile head,while the porosity of saturated soil beneath the pile toe has significant effects both on the resonance amplitude and the resonance frequency of the dynamic impedance at the pile head.
In order to study the longitudinal vibration characteristics of floating piles in saturated soil,a saturated virtual soil pile model based on Biot′s wave theory was proposed,and a coupled longitudinal vibration system of three-dimensional saturated layered soil,virtual soil piles and solid piles was established. The analytical solution of the displacement of saturated soil was derived by potential function method,and the vertical dynamic impedance at the pile head was obtained by using the pile-soil compatibility conditions and the transfer method of impedance function. The validity of the obtained solution was verified by degrading to existing solutions,and parametric analyses were performed to investigate the effects of the parameters of the saturated soil on the vibration characteristics at the pile head. The results show that,when the saturation of soil layers beneath the pile toe is remarkable and the drainage is poor,the saturated virtual soil pile model and the relevant analytical solution is more suitable to analyze the longitudinal vibration characteristics of floating piles. The longitudinal interlayer of surrounding soil has obvious effect on the amplitude of the dynamic impedance at the pile head,but the effect of longitudinal interlayer of soil beneath the pile toe on the dynamic impedance at the pile head can be ignored. The porosity of saturated surface surrounding soil has obvious influence only on the resonance amplitude of the dynamic impedance at the pile head,while the porosity of saturated soil beneath the pile toe has significant effects both on the resonance amplitude and the resonance frequency of the dynamic impedance at the pile head.
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 Chunyi,ZHANG Shiping,YANG Gang,et al.Vertical vibration of floating piles in saturated viscoelastic halfspaceconsidering wave effect of subsoil under pile bottom[J].Chinese Journal of Geotechnical Engineering,2015,37(5):878-892.(in Chinese))
[2]ZHENG C J,KOURETZIS G P,SLOAN S W,et al.Vertical vibration of an elastic pile embedded in poroelastic soil[J].Soil Dynamics and Earthquake Engineering,2015,77:177-181.
[3]ZHOU X L,WANG J H,JIANG L F,et al.Transient dynamic response of pile to vertical load in saturated soil[J].Mechanics Research Communications,2009,36(5):618-624.
[4]刘林超,杨骁.基于多孔介质理论的饱和土-桩纵向耦合振动研究[J].土木工程学报,2009,42(9):89-95.(LIU Linchao,YANGXiao.Study of vertical coupled vibrations of piles in saturated soils using porous medium theory[J].China Civil Engineering Journal,2009,42(9):89-95.(in Chinese))
[5]崔春义,孟坤,武亚军,等.考虑竖向波动效应的径向非均质黏性阻尼土中管桩纵向振动响应研究[J].岩土工程学报,2018,40(8):1 434-1 443.(CUI Chunyi,MENG Kun,WU Yajun,et al.Dynamic response of vertical vibration of pipe pile in soil with radial inhomogeneousity and viscous damping considering vertical wave effect[J].Chinese Journal of Geotechnical Engineering,2018,40(8):1 434-1 443.(in Chinese))
[6]NOVAK M.Dynamic stiffness and damping of piles[J].Canadian Geotechnical Journal,1974,11(4):574-598.
[7]NOVAK M,BEREDUGO Y O.Vertical vibration of embedded footings[J].Soil Mechanics and Foundation Division,1972,98(12):1 291-1 131.
[8]NOGAMI T,NOVAK M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering and Structural Dynamics,1976,4(3):277-293.
[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.(HUChangbin,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))
[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):1 363-1 370.(WANG Kuihua,QUE Renbo,XIA Jianzhong.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):1 363-1 370.(in Chinese))
[11]陈龙珠,陈胜立.饱和地基上刚性基础的竖向振动分析[J].岩土工程学报,1999,21(4):392-397.(CHEN Longzhu,CHNE Shengli.Vertical vibration of a rigid circular footing on saturated soil[J].Chinese Journal of Geotechnical Engineering,1999,21(4):392-397.(in Chinese))
[12]WANG J H,ZHOU X L,LU J F.Dynamic response of pile groups embedded in a poroelastic medium[J].Soil Dynamics and Earthquake Engineering,2003,23(3):53-60.
[13]蔡袁强,胡秀青.饱和地基中埋置刚性圆柱基础的等效竖向动力刚度[J].岩石力学与工程学报,2008,27(2):361-367.(CAIYuanqiang,HU Xiuqing.Equivalent vertical dynamic stiffness for embedded rigid cylindrical foundation in saturated soil[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(2):361-367.(in Chinese))
[14]CAI Y Q,HU X Q,XU C J,et al.Vertical dynamic response of a rigid foundation embedded in a poroelastic soil layer[J].International Journal for Numerical and Analytical Methods in Geomechanics,2009,33(11):1 363-1 388.
[15]BIOT M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33(4):1 482-1 498.
[16]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,XIEKanghe.Vertical vibration of an end bearing pile embedded in saturated soil[J].Chinese Journal of Theoretical and Applied Mechanics,2004,36(4):435-442.(in Chinese))
[17]余俊,尚守平,任慧,等.饱和土中桩竖向振动响应分析[J].工程力学,2008,25(10):187-193.(YU Jun,SHANG Shouping,REN Hui,et al.Vertical dynamic response of pile in saturated soil[J].Engineering Mechanics,2008,25(10):187-193.(in Chinese))
[18]NOGAMI T,KONAGAI K.Time domain axial response of dynamically loaded single piles[J].Journal of Engineering Mechanics,1986,113(3):1 512-1 525.
[19]王奎华,谢康和,曾国熙.有限长桩受迫振动问题解析解及其应用[J].岩土工程学报,1997,19(6):27-35.(WANG Kuihua,XIE Kanghe,ZENG Guoxi.Analytical solution to vibfration of finite length pile under exciting force and its application[J].Chinese Journal of Geotechnical Engineering,1997,19(6):27-35.(in Chinese))
[20]WANG K H,WU W B,ZHANG Z Q,et al.Vertical dynamic response of an inhomogeneous viscoelastic pile[J].Computers and Geotechnics,2010,37(4):536-544.
[21]CUI C Y,ZHANG S P,DAVID C,et al.Dynamic impedance of a floating pile embedded in poro-visco-elastic soils subjected to vertical harmonic loads[J].Geomechanics and Engineering,2018,15(2):793-803.
[22]MUKI R,STERNBERG E.Elastostatic load transfer to a half space from a partially embedded axially loaded rod[J].International Journal of Solids and Structures,1970,6(1):69-90.
[23]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.
[24]SENJUNTICHAI T,MANI S,RAJAPAKSE R K N D.Vertical vibration of an embedded rigid foundation in a poroelastic soil[J].Soil Dynamics and Earthquake Engineering,2006,26(6/7):626-636.
[25]LU J F,JIANG D S,NIE W.Dynamic response of a pile embedded in a porous medium subjected to plane SH waves[J].Computers and Geotechnics,2006,33(8):404-418.
[26]杨冬英,王奎华.非均质土中基于虚土桩法的桩基纵向振动[J].浙江大学学报:工学版,2010,44(10):2 021-2 028.(YANG Dongying,WANG Kuihua.Vertical vibration of pile based on fictitious soil-pile model in inhomogeneous soil[J].Journal of Zhejiang University:Engineering Science,2010,44(10):2 021-2 028.(in Chinese))
[27]NOGAMI T.Dynamic group effect in axial response of grouped piles[J].Journal of Geotechnical Engineering,1983,109(2):228-243.
[28]吴文兵,王奎华,杨冬英,等.成层土中基于虚土桩模型的桩基纵向振动响应[J].中国公路学报,2012,25(2):72-80.(WU Wenbing,WANG Kuihua,YANG Dongying,et al.Longitudinal dynamic response to the pile embedded in layered soil based on fictitious soil pile model[J].China Journal of Highway and Transport,2012,25(2):72-80.(in Chinese))
[29]王宁,王奎华.桩底土的成层性对桩体纵向刚度的影响[J].岩石力学与工程学报,2013,32(5):1 042-1 048.(WANG Ning,WANGKuihua.Influence of layering of stratum under pile tip on pile longitudinal stiffness[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(5):1 042-1 048.(in Chinese))
[30]门福录.波在飽水孔隙弹性介质中的传播[J].地球物理学报,1965,(2):37-44.(MEN Fulu.Wave propagation in a porous,saturated elastic medium[J].Chinese Journal of Geophysics,1965,(2):37-44.(in Chinese))
[31]李鹏,宋二祥.渗透系数极端情况下饱和土中压缩波波速及其物理本质[J].岩土力学,2012,33(7):1 979-1 985.(LI Peng,SONGEerxiang.Compressional wave velocity and its physical nature in saturated soils with extreme permeability values[J].Rock and Soil Mechanics,2012,33(7):1 979-1 985.(in Chinese))
[32]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 Qiang,WANGKuihua,XIE Kanghe.Dynamic response for vertical vibration of large diameter pile in saturated soil[J].Journal of Vibration Engineering,2005,18(4):500-505.(in Chinese))
[33]王奎华,王宁,刘凯,等.三维轴对称条件下基于虚土桩法的单桩纵向振动分析[J].岩土工程学报,2012,34(5):885-892.(WANG Kuihua,WANG Ning,LIU Kai,et al.Longitudinal vibration of piles in 3D axisymmetric soil based on fictitious soil pile method[J].Chinese Journal of Geotechnical Engineering,2012,34(5):885-892.(in Chinese))
[2]ZHENG C J,KOURETZIS G P,SLOAN S W,et al.Vertical vibration of an elastic pile embedded in poroelastic soil[J].Soil Dynamics and Earthquake Engineering,2015,77:177-181.
[3]ZHOU X L,WANG J H,JIANG L F,et al.Transient dynamic response of pile to vertical load in saturated soil[J].Mechanics Research Communications,2009,36(5):618-624.
[4]刘林超,杨骁.基于多孔介质理论的饱和土-桩纵向耦合振动研究[J].土木工程学报,2009,42(9):89-95.(LIU Linchao,YANGXiao.Study of vertical coupled vibrations of piles in saturated soils using porous medium theory[J].China Civil Engineering Journal,2009,42(9):89-95.(in Chinese))
[5]崔春义,孟坤,武亚军,等.考虑竖向波动效应的径向非均质黏性阻尼土中管桩纵向振动响应研究[J].岩土工程学报,2018,40(8):1 434-1 443.(CUI Chunyi,MENG Kun,WU Yajun,et al.Dynamic response of vertical vibration of pipe pile in soil with radial inhomogeneousity and viscous damping considering vertical wave effect[J].Chinese Journal of Geotechnical Engineering,2018,40(8):1 434-1 443.(in Chinese))
[6]NOVAK M.Dynamic stiffness and damping of piles[J].Canadian Geotechnical Journal,1974,11(4):574-598.
[7]NOVAK M,BEREDUGO Y O.Vertical vibration of embedded footings[J].Soil Mechanics and Foundation Division,1972,98(12):1 291-1 131.
[8]NOGAMI T,NOVAK M.Soil-pile interaction in vertical vibration[J].Earthquake Engineering and Structural Dynamics,1976,4(3):277-293.
[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.(HUChangbin,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))
[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):1 363-1 370.(WANG Kuihua,QUE Renbo,XIA Jianzhong.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):1 363-1 370.(in Chinese))
[11]陈龙珠,陈胜立.饱和地基上刚性基础的竖向振动分析[J].岩土工程学报,1999,21(4):392-397.(CHEN Longzhu,CHNE Shengli.Vertical vibration of a rigid circular footing on saturated soil[J].Chinese Journal of Geotechnical Engineering,1999,21(4):392-397.(in Chinese))
[12]WANG J H,ZHOU X L,LU J F.Dynamic response of pile groups embedded in a poroelastic medium[J].Soil Dynamics and Earthquake Engineering,2003,23(3):53-60.
[13]蔡袁强,胡秀青.饱和地基中埋置刚性圆柱基础的等效竖向动力刚度[J].岩石力学与工程学报,2008,27(2):361-367.(CAIYuanqiang,HU Xiuqing.Equivalent vertical dynamic stiffness for embedded rigid cylindrical foundation in saturated soil[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(2):361-367.(in Chinese))
[14]CAI Y Q,HU X Q,XU C J,et al.Vertical dynamic response of a rigid foundation embedded in a poroelastic soil layer[J].International Journal for Numerical and Analytical Methods in Geomechanics,2009,33(11):1 363-1 388.
[15]BIOT M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33(4):1 482-1 498.
[16]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,XIEKanghe.Vertical vibration of an end bearing pile embedded in saturated soil[J].Chinese Journal of Theoretical and Applied Mechanics,2004,36(4):435-442.(in Chinese))
[17]余俊,尚守平,任慧,等.饱和土中桩竖向振动响应分析[J].工程力学,2008,25(10):187-193.(YU Jun,SHANG Shouping,REN Hui,et al.Vertical dynamic response of pile in saturated soil[J].Engineering Mechanics,2008,25(10):187-193.(in Chinese))
[18]NOGAMI T,KONAGAI K.Time domain axial response of dynamically loaded single piles[J].Journal of Engineering Mechanics,1986,113(3):1 512-1 525.
[19]王奎华,谢康和,曾国熙.有限长桩受迫振动问题解析解及其应用[J].岩土工程学报,1997,19(6):27-35.(WANG Kuihua,XIE Kanghe,ZENG Guoxi.Analytical solution to vibfration of finite length pile under exciting force and its application[J].Chinese Journal of Geotechnical Engineering,1997,19(6):27-35.(in Chinese))
[20]WANG K H,WU W B,ZHANG Z Q,et al.Vertical dynamic response of an inhomogeneous viscoelastic pile[J].Computers and Geotechnics,2010,37(4):536-544.
[21]CUI C Y,ZHANG S P,DAVID C,et al.Dynamic impedance of a floating pile embedded in poro-visco-elastic soils subjected to vertical harmonic loads[J].Geomechanics and Engineering,2018,15(2):793-803.
[22]MUKI R,STERNBERG E.Elastostatic load transfer to a half space from a partially embedded axially loaded rod[J].International Journal of Solids and Structures,1970,6(1):69-90.
[23]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.
[24]SENJUNTICHAI T,MANI S,RAJAPAKSE R K N D.Vertical vibration of an embedded rigid foundation in a poroelastic soil[J].Soil Dynamics and Earthquake Engineering,2006,26(6/7):626-636.
[25]LU J F,JIANG D S,NIE W.Dynamic response of a pile embedded in a porous medium subjected to plane SH waves[J].Computers and Geotechnics,2006,33(8):404-418.
[26]杨冬英,王奎华.非均质土中基于虚土桩法的桩基纵向振动[J].浙江大学学报:工学版,2010,44(10):2 021-2 028.(YANG Dongying,WANG Kuihua.Vertical vibration of pile based on fictitious soil-pile model in inhomogeneous soil[J].Journal of Zhejiang University:Engineering Science,2010,44(10):2 021-2 028.(in Chinese))
[27]NOGAMI T.Dynamic group effect in axial response of grouped piles[J].Journal of Geotechnical Engineering,1983,109(2):228-243.
[28]吴文兵,王奎华,杨冬英,等.成层土中基于虚土桩模型的桩基纵向振动响应[J].中国公路学报,2012,25(2):72-80.(WU Wenbing,WANG Kuihua,YANG Dongying,et al.Longitudinal dynamic response to the pile embedded in layered soil based on fictitious soil pile model[J].China Journal of Highway and Transport,2012,25(2):72-80.(in Chinese))
[29]王宁,王奎华.桩底土的成层性对桩体纵向刚度的影响[J].岩石力学与工程学报,2013,32(5):1 042-1 048.(WANG Ning,WANGKuihua.Influence of layering of stratum under pile tip on pile longitudinal stiffness[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(5):1 042-1 048.(in Chinese))
[30]门福录.波在飽水孔隙弹性介质中的传播[J].地球物理学报,1965,(2):37-44.(MEN Fulu.Wave propagation in a porous,saturated elastic medium[J].Chinese Journal of Geophysics,1965,(2):37-44.(in Chinese))
[31]李鹏,宋二祥.渗透系数极端情况下饱和土中压缩波波速及其物理本质[J].岩土力学,2012,33(7):1 979-1 985.(LI Peng,SONGEerxiang.Compressional wave velocity and its physical nature in saturated soils with extreme permeability values[J].Rock and Soil Mechanics,2012,33(7):1 979-1 985.(in Chinese))
[32]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 Qiang,WANGKuihua,XIE Kanghe.Dynamic response for vertical vibration of large diameter pile in saturated soil[J].Journal of Vibration Engineering,2005,18(4):500-505.(in Chinese))
[33]王奎华,王宁,刘凯,等.三维轴对称条件下基于虚土桩法的单桩纵向振动分析[J].岩土工程学报,2012,34(5):885-892.(WANG Kuihua,WANG Ning,LIU Kai,et al.Longitudinal vibration of piles in 3D axisymmetric soil based on fictitious soil pile method[J].Chinese Journal of Geotechnical Engineering,2012,34(5):885-892.(in Chinese))
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