考虑横向惯性效应时楔形桩纵向振动阻抗研究
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摘要
基于Rayleigh-Love杆模型,研究考虑横向惯性效应时成层土中楔形桩的纵向振动问题。首先,根据桩周土的成层性并考虑楔形桩的变截面特性,将桩土系统沿纵向划分为有限个微元段。然后,运用Laplace变换技术和阻抗函数递推方法,在平面应变条件下推导得到成层土中楔形桩纵向振动时桩顶复阻抗的解析解。最后,采用参数研究方法,在低频范围内分析楔形桩设计参数对桩顶复阻抗的影响,并将同体积时的楔形桩与均匀截面桩的桩顶复阻抗进行对比。结果表明:(1)楔形桩其他设计参数不变时,动阻尼随着楔角的增大而增大,动刚度也随着楔角的增大而增大,但增大的幅度会随着频率的增大而逐渐减小;(2)楔形桩其他设计参数不变时,动刚度随着桩长的增大而减小,动阻尼随着桩长的增大而增大;(3)对等体积的楔形桩与均匀截面桩,当桩长相同时,楔角越大,动刚度越小,动阻尼越大;当桩端截面积相同时,楔角越大,动刚度越大,动阻尼先增大再减小。
Based on Rayleigh-Love rode model,the longitudinal vibration of tapered pile embedded in layered soil is theoretically investigated by considering lateral inertial effect of tapered pile.At first,considering stratification of the surrounding soil and variable cross-section of the tapered pile,the pile-soil system is discretized into finite segments.Then,by virtue of Laplace technique and impedance function transfer method,the analytical solution of complex impedance of tapered pile under longitudinal exciting force is derived.Finally,by means of parametric study method,the influence of the design parameters of tapered pile on complex impedance at the pile head is investigated within the low frequency range,and the complex impedance of tapered pile is compared with that of uniform cross-section pile with same volume.The results show that:(1) When other design parameters of tapered pile remain unchanged,dynamic damping increases as the cone-angle increases,dynamic stiffness also increases as the cone-angle increases,but the increase magnitude decreases gradually as the frequency increases;(2) When other design parameters of tapered pile remain unchanged,dynamic stiffness decreases as the cone-angle increases,and dynamic damping increases as the cone-angle increases;(3) When the volume and length of tapered pile are the same as that of uniform cross-section pile,dynamic stiffness decreases as the cone-angle increases,and dynamic damping increases as the cone-angle increases.When the volume and radius at the pile tip of tapered pile are the same as that of uniform cross-section pile,dynamic stiffness increases as the cone-angle of tapered pile increases,and dynamic damping increases as the cone-angle increases within a small range of cone-angle.
Based on Rayleigh-Love rode model,the longitudinal vibration of tapered pile embedded in layered soil is theoretically investigated by considering lateral inertial effect of tapered pile.At first,considering stratification of the surrounding soil and variable cross-section of the tapered pile,the pile-soil system is discretized into finite segments.Then,by virtue of Laplace technique and impedance function transfer method,the analytical solution of complex impedance of tapered pile under longitudinal exciting force is derived.Finally,by means of parametric study method,the influence of the design parameters of tapered pile on complex impedance at the pile head is investigated within the low frequency range,and the complex impedance of tapered pile is compared with that of uniform cross-section pile with same volume.The results show that:(1) When other design parameters of tapered pile remain unchanged,dynamic damping increases as the cone-angle increases,dynamic stiffness also increases as the cone-angle increases,but the increase magnitude decreases gradually as the frequency increases;(2) When other design parameters of tapered pile remain unchanged,dynamic stiffness decreases as the cone-angle increases,and dynamic damping increases as the cone-angle increases;(3) When the volume and length of tapered pile are the same as that of uniform cross-section pile,dynamic stiffness decreases as the cone-angle increases,and dynamic damping increases as the cone-angle increases.When the volume and radius at the pile tip of tapered pile are the same as that of uniform cross-section pile,dynamic stiffness increases as the cone-angle of tapered pile increases,and dynamic damping increases as the cone-angle increases within a small range of cone-angle.
引文
[1]WEI J Q,HESHAM M.Experimental study of axial behaviour of tapered piles[J].Canadian Geotechnical Journal,1998,35(4):641–654.
[2]RYBNIKOV A M.Experimental investigation of bearing capacity of第30卷增2吴文兵等:考虑横向惯性效应时楔形桩纵向振动阻抗研究?3625?bored-case in place tapered piles[J].Soil Mechanics and Foundation Engineering,1990,27(2):48–51.
[3]蒋建平,高广运.扩底桩、楔形桩、等直径桩对比试验研究[J].岩土工程学报,2003,25(6):764–766.(JIANG Jianping,GAO Guangyun.Comparison of belled pile,tapered pile and equal-diameter pile[J].Chinese Journal of Geotechnical Engineering,2003,25(6):764–766.(in Chinese))
[4]刘杰,王忠海.楔形桩承载力试验研究[J].天津大学学报,2002,35(2):257–260.(LIU Jie,WANG Zhonghai.Experimental study on the bearing capacity of wedge pile[J].Journal of Tianjin University,2002,35(2):257–260.(in Chinese))
[5]何杰,刘杰,陈科良,等.静压楔形桩挤土效应的室内模型试验[J].工业建筑,2008,38(1):74–75.(HE Jie,LIU Jie,CHEN Keliang,et al.Experiment of compacting effects of static piling in clay ground with tapered pile[J].Industrial Construction,2008,38(1):74–75.(in Chinese))
[6]KODIKARA J K,MOORE I D.Axial response of tapered piles in cohesive frictional ground[J].Journal of Geotechnical and Geoenvironmental Engineering,1993,119(4):675–693.
[7]EI NAGGAR M H,WEI J Q.Uplift behaviour of tapered piles established from model tests[J].Canadian Geotechnical Journal,2000,37(1):56–74.
[8]刘杰,何杰,闵长青.楔形桩与圆柱形桩复合地基承载性状对比研究[J].岩土力学,2010,31(7):2 202–2 206.(LIU Jie,HE Jie,MIN Changqing.Contrast research of bearing behavior for composite foundation with tapered piles and cylindrical piles[J].Rock and Soil Mechanics,2010,31(7):2 202–2 206.(in Chinese))
[9]刘杰,何杰,闵长青.楔形刚性桩与桩周土的非线性相互作用[J].铁道学报,2010,32(2):137–140.(LIU Jie,HE Jie,MIN Changqing.Nonlinear interaction between the rigid taper pile and pile surrounding soil[J].Journal of the China Railway Society,2010,32(2):137–140.(in Chinese))
[10]TAKE W A,WALSANGKAR A J.The elastic analysis of compressible tin-piles and pile groups[J].Geotechnique,2002,31(4):456–474.
[11]MOHAMEDZEIN Y E,MOHAMED M G.Finite analysis of axially tin-pile groups[J].Computers and Geotechanics,2001,26(2):231–243.
[12]GOUGH W,RICHARDS J P G,WILLIAMS R P.Vibration and Waves[M].New York,USA:Halsted Press of John Wiley and Sons,1983:175–181.
[13]KOTEN H V,MIDDENDORP O,BREDERODE P V.An analysis of dissipative wave propagation in a pile[C]//Proceedings of the International Seminar on the Application of Stress-Wave Theory on Piles.[S.l.]:[s.n.],1980:23–40.
[14]王奎华,谢康和,曾国熙.有限长桩受迫振动问题解析解及应用[J].岩土工程学报,1997,19(6):27–35.(WANG Kuihua,XIE Kanghe,ZENG Guoxi.Analytical solution to vibration of finite length pile under exciting force and its application[J].Chinese Journal of Geotechnical Engineering,1997,19(6):27–35.(in Chinese))
[15]NOVAK M,ABOUL-ELLA F.Impedance functions of piles in layered media[J].Journal of the Engineering Mechanical Division,1978,104(3):643–661.
[16]NOVAK M,NOGAMI T,ABOUL-ELLA F.Dynamic soil reaction for plane strain case[J].Journal of the Engineering Mechanical Division,1978,104(4):953–959.
[17]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):1 362–1 370.(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):1 362–1 370.(in Chinese))
[18]胡昌斌,张涛.桩与滞回阻尼土相互作用时桩基扭转振动时域响应分析[J].岩石力学与工程学报,2006,25(增1):3 190–3 197.(HU Changbin,ZHANG Tao.Time domain torsional response of dynamically loaded pile in hysteretic type damping soil layer[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(Supp.1):3 190–3 197.(in Chinese))
[19]王海东,尚守平.瑞利波作用下径向非匀质地基中的单桩竖向响应研究[J].振动工程学报,2006,19(2):258–264.(WANG Haidong,SHANG Shouping.Research on vertical dynamic response of single-pile in radically inhomogeneous soil during the passage of Rayleigh waves[J].Journal of Vibration Engineering,2006,19(2):258–264.(in Chinese))
[20]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 Desen,LUAN Maotian,YANG Qing.Review of dynamic Winkler model appfied in pile-soil interaction analyses[J].World Earthquake Engineering,2005,21(1):12–17.(in Chinese))
[21]刘东甲.完整桩瞬态纵向振动的参数影响研究[J].合肥工业大学学报:自然科学版,2000,23(6):1 014–1 018.(LIU Dongjia.Analysis of influence of dynamic model parameters of an integrate pile on its transient longitudinal vibration[J].Journal of Hefei University of Technology:Natural Science,2000,23(6):1 014–1 018.(in Chinese))
[22]黎正根,龚育龄.波在大直径桩中传播的三维效应现象[J].岩石力学与工程学报,1998,17(4):434–439.(LI Zhenggen,GONG Yuling.Discussion on three-dimensional effect of wave propagating in the pile with large diameter[J].Chinese Journal of Rock Mechanics and Engineering,1998,17(4):434–439.(in Chinese))
[23]POPOVICS J S.Effects of Poisson′s ratio on impact-echo test analysis[J].Journal of Engineering Mechanics,1997,123(8):843–851.
[2]RYBNIKOV A M.Experimental investigation of bearing capacity of第30卷增2吴文兵等:考虑横向惯性效应时楔形桩纵向振动阻抗研究?3625?bored-case in place tapered piles[J].Soil Mechanics and Foundation Engineering,1990,27(2):48–51.
[3]蒋建平,高广运.扩底桩、楔形桩、等直径桩对比试验研究[J].岩土工程学报,2003,25(6):764–766.(JIANG Jianping,GAO Guangyun.Comparison of belled pile,tapered pile and equal-diameter pile[J].Chinese Journal of Geotechnical Engineering,2003,25(6):764–766.(in Chinese))
[4]刘杰,王忠海.楔形桩承载力试验研究[J].天津大学学报,2002,35(2):257–260.(LIU Jie,WANG Zhonghai.Experimental study on the bearing capacity of wedge pile[J].Journal of Tianjin University,2002,35(2):257–260.(in Chinese))
[5]何杰,刘杰,陈科良,等.静压楔形桩挤土效应的室内模型试验[J].工业建筑,2008,38(1):74–75.(HE Jie,LIU Jie,CHEN Keliang,et al.Experiment of compacting effects of static piling in clay ground with tapered pile[J].Industrial Construction,2008,38(1):74–75.(in Chinese))
[6]KODIKARA J K,MOORE I D.Axial response of tapered piles in cohesive frictional ground[J].Journal of Geotechnical and Geoenvironmental Engineering,1993,119(4):675–693.
[7]EI NAGGAR M H,WEI J Q.Uplift behaviour of tapered piles established from model tests[J].Canadian Geotechnical Journal,2000,37(1):56–74.
[8]刘杰,何杰,闵长青.楔形桩与圆柱形桩复合地基承载性状对比研究[J].岩土力学,2010,31(7):2 202–2 206.(LIU Jie,HE Jie,MIN Changqing.Contrast research of bearing behavior for composite foundation with tapered piles and cylindrical piles[J].Rock and Soil Mechanics,2010,31(7):2 202–2 206.(in Chinese))
[9]刘杰,何杰,闵长青.楔形刚性桩与桩周土的非线性相互作用[J].铁道学报,2010,32(2):137–140.(LIU Jie,HE Jie,MIN Changqing.Nonlinear interaction between the rigid taper pile and pile surrounding soil[J].Journal of the China Railway Society,2010,32(2):137–140.(in Chinese))
[10]TAKE W A,WALSANGKAR A J.The elastic analysis of compressible tin-piles and pile groups[J].Geotechnique,2002,31(4):456–474.
[11]MOHAMEDZEIN Y E,MOHAMED M G.Finite analysis of axially tin-pile groups[J].Computers and Geotechanics,2001,26(2):231–243.
[12]GOUGH W,RICHARDS J P G,WILLIAMS R P.Vibration and Waves[M].New York,USA:Halsted Press of John Wiley and Sons,1983:175–181.
[13]KOTEN H V,MIDDENDORP O,BREDERODE P V.An analysis of dissipative wave propagation in a pile[C]//Proceedings of the International Seminar on the Application of Stress-Wave Theory on Piles.[S.l.]:[s.n.],1980:23–40.
[14]王奎华,谢康和,曾国熙.有限长桩受迫振动问题解析解及应用[J].岩土工程学报,1997,19(6):27–35.(WANG Kuihua,XIE Kanghe,ZENG Guoxi.Analytical solution to vibration of finite length pile under exciting force and its application[J].Chinese Journal of Geotechnical Engineering,1997,19(6):27–35.(in Chinese))
[15]NOVAK M,ABOUL-ELLA F.Impedance functions of piles in layered media[J].Journal of the Engineering Mechanical Division,1978,104(3):643–661.
[16]NOVAK M,NOGAMI T,ABOUL-ELLA F.Dynamic soil reaction for plane strain case[J].Journal of the Engineering Mechanical Division,1978,104(4):953–959.
[17]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):1 362–1 370.(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):1 362–1 370.(in Chinese))
[18]胡昌斌,张涛.桩与滞回阻尼土相互作用时桩基扭转振动时域响应分析[J].岩石力学与工程学报,2006,25(增1):3 190–3 197.(HU Changbin,ZHANG Tao.Time domain torsional response of dynamically loaded pile in hysteretic type damping soil layer[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(Supp.1):3 190–3 197.(in Chinese))
[19]王海东,尚守平.瑞利波作用下径向非匀质地基中的单桩竖向响应研究[J].振动工程学报,2006,19(2):258–264.(WANG Haidong,SHANG Shouping.Research on vertical dynamic response of single-pile in radically inhomogeneous soil during the passage of Rayleigh waves[J].Journal of Vibration Engineering,2006,19(2):258–264.(in Chinese))
[20]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 Desen,LUAN Maotian,YANG Qing.Review of dynamic Winkler model appfied in pile-soil interaction analyses[J].World Earthquake Engineering,2005,21(1):12–17.(in Chinese))
[21]刘东甲.完整桩瞬态纵向振动的参数影响研究[J].合肥工业大学学报:自然科学版,2000,23(6):1 014–1 018.(LIU Dongjia.Analysis of influence of dynamic model parameters of an integrate pile on its transient longitudinal vibration[J].Journal of Hefei University of Technology:Natural Science,2000,23(6):1 014–1 018.(in Chinese))
[22]黎正根,龚育龄.波在大直径桩中传播的三维效应现象[J].岩石力学与工程学报,1998,17(4):434–439.(LI Zhenggen,GONG Yuling.Discussion on three-dimensional effect of wave propagating in the pile with large diameter[J].Chinese Journal of Rock Mechanics and Engineering,1998,17(4):434–439.(in Chinese))
[23]POPOVICS J S.Effects of Poisson′s ratio on impact-echo test analysis[J].Journal of Engineering Mechanics,1997,123(8):843–851.
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