楔形桩桩顶纵向振动阻抗的解析解
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摘要
针对成层地基中楔形桩的纵向振动问题,采用平面应变模型模拟桩侧土,并根据桩侧土的成层性及考虑楔形桩的变截面特性,将桩土系统划分为有限个微元段,运用Laplace变换技术和阻抗函数递推方法,求得了楔形桩纵向振动情况下桩顶复阻抗的解析解,并讨论了楔角对楔形桩桩顶复阻抗的影响。结果表明,动刚度曲线和动阻尼曲线的共振峰幅值均随楔角的增大而变大;当其他参数不变仅桩长变化时,动刚度曲线的共振峰幅值随桩长增大而变小,动阻尼曲线的共振峰幅值随桩长增大而变大;当其他参数不变仅桩端截面半径变化时,动刚度曲线和动阻尼曲线的共振峰幅值随桩端截面半径增大而变大。
The longitudinal dynamic complex impedance of tapered piles in layered ground is investigated.Assuming the surrounding soil to be plane strain model and considering variable cross-section of the tapered piles and stratification of the surrounding soil,the pile-soil system is discretized into finite segments.Then,by means of the Laplace technique and the impedance function transfer method,the analytical solution of complex stiffness of the tapered piles under vertical exciting force is derived.Additionally,by means of parametric study method,the influence of the cone angle on the complex stiffness at the pile top is investigated.It is shown that the amplitudes of resonance peak of dynamic stiffness curve and dynamic damping curve increase as the cone angle increases.When the length of tapered piles is variable and other parameters are unaltered,the amplitude of resonance peak of dynamic stiffness curve decreases as the cone angel increases and the amplitude of resonance peak of dynamic curve increases as the cone angel increases.When the radius of tapered pile tip is variable and other parameters are unaltered,the amplitudes of resonance peak of dynamic stiffness curve and dynamic damping curve increase as the radius of tapered pile tip increases.
The longitudinal dynamic complex impedance of tapered piles in layered ground is investigated.Assuming the surrounding soil to be plane strain model and considering variable cross-section of the tapered piles and stratification of the surrounding soil,the pile-soil system is discretized into finite segments.Then,by means of the Laplace technique and the impedance function transfer method,the analytical solution of complex stiffness of the tapered piles under vertical exciting force is derived.Additionally,by means of parametric study method,the influence of the cone angle on the complex stiffness at the pile top is investigated.It is shown that the amplitudes of resonance peak of dynamic stiffness curve and dynamic damping curve increase as the cone angle increases.When the length of tapered piles is variable and other parameters are unaltered,the amplitude of resonance peak of dynamic stiffness curve decreases as the cone angel increases and the amplitude of resonance peak of dynamic curve increases as the cone angel increases.When the radius of tapered pile tip is variable and other parameters are unaltered,the amplitudes of resonance peak of dynamic stiffness curve and dynamic damping curve increase as the radius of tapered pile tip increases.
引文
[1]ZIL’BERBERG S D,Sherstnev A D.Construction ofcompaction tapered pile foundation[J].Soil Mechanics andFoundation Engineering,1990,27(3):96–101.
[2]EI NAGGAR M H,WEI J Q.Experimental study of axialbehavior of tapered pile[J].Canadian Geotechnical Journal,1998,35:641–654.
[3]EI NAGGAR M H,MOHAMMED S.Evaluation of axialperformance of tapered piles from centrifuge tests[J].Canadian Geotechnical Journal,2000,37(6):1295–1308.
[4]WEI J Q.Experimental investigation of tapered piles[D].Ontario:The University of Western Ontario,1998.
[5]MOHAMMED S,EI NAGGAR M H,MONCEF N.Loadtransfer of fiber-reinforced polymer(FRP)composite taperedpiles in dense sand[J].Canadian Geotechnical Journal,2004,41(1):70–95.
[6]蒋建平,高广运,顾宝和.扩底桩、楔形桩、等直径桩对比试验研究[J].岩土工程学报,2003,26(6):764–766.(JIANG Jian-ping,GAO Guang-yun,GU Bao-he.Comparison of belled pile,tapered pile and equal-diameterpile[J].Chinese Journal of Geotechnical Engineering,2003,26(6):764–766.(in Chinese))
[7]刘杰,王忠海.楔形桩承载力实验研究[J].天津大学学报,2002,35(4):257–260.(LIU Jie,WANG Zhong-hai.Experimental study on the bearing capacity of wedge pile[J].Journal of Tianjin University,2002,35(4):257–260.(inChinese))
[8]王奎华,吴文兵,叶良,等.基于极限平衡理论的楔形桩承载力计算方法[J].建筑科学与工程学报,2009,26(4):108–113.(WANG Kui-hua,WU Wen-bing,YE Liang,et al.Calculation method of bearing capacity of tapered pile basedon limit equilibrium theory[J].Journal of Architecture andCivil Engineering,2009,26(4):108–113.(in Chinese))
[9]刘杰,何杰,闵长青.楔形刚性桩复合地基中桩的最佳楔角范围研究[J].工程力学,2009,10(增刊1):293–299.(LIU Jie,HE Jie,MIN Chang-qing.Study of the rationalwedge angle range in a composite foundation with stifftapered piles[J].Engineering Mechanics,2009,10(S1):293–299.(in Chinese))
[10]刘杰,何杰,闵长青.楔形桩与圆柱形桩复合地基承载形状对比研究[J].岩土力学,2010,31(7):2202–2206.(LIU Jie,HE Jie,MIN Chang-qing.Contrast research ofbearing behavior for composite foundation with tapered pilesand cylindrical piles[J].Rock and Soil Mechanics,2010,31(7):2202–2206.(in Chinese))
[11]刘杰,何杰,闵长青.夯实水泥土楔形桩复合地基中桩的合理楔角范围研究[J].土木工程学报,2010,43(6):122–127.(LIU Jie,HE Jie,MIN Chang-qing.Study of therational wedge angle range in a composite foundation withrammed soil-cement tapered piles[J].China CivilEngineering Journal,2010,43(6):122–127.(in Chinese))
[12]GOUGH W,RICHARDS J P G.,WILLIAMS R P.Vibrationand waves[M].New York:Halsted Press of John Wiley&Sons,1983.
[13]VAN KOTEN H,MIDDENDORP P,VAN BREDERODE P.An analysis of dissipative wave propagation in a pile[C]//IntSeminar on the Application of Stress-Wave Theory on Piles,Stockholm,1980:210–215.
[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.(WANGKui-hua,XIE Kang-he,ZENG Guo-xi.Analytical solution tovibration of finite length pile under exciting force and itsapplication[J].Chinese Journal of Geotechnical Engineering,1997,19(6):27–35.(in Chinese))
[15]王奎华,李冰河,谢康和,等.弹性支承桩受迫振动问题广义函数解及应用[J].浙江大学学报(自然科学版),1998,32(5):545–551.(WANG Kui-hua,LI Bing-he,XIE Kang-he,et al.A generalized solution to the vibration of elasticsupporting foundation pile under exciting force and itsapplication[J].Journal of Zhejiang University(NaturalScience),1998,32(5):545–551.(in Chinese))
[16]王奎华,谢康和,曾国熙.变截面阻抗桩受迫振动问题解析解及应用[J].土木工程学报,1998,31(6):56–67.(WANG Kui-hua,XIE Kang-he,ZENG Guo-xi.Ananalytical solution to force vibration of foundation pile withvariable section impedance and its application[J].China CivilEngineering Journal,1998,31(6):56–67.(in Chinese))
[17]NOVAK M,ABOUL-ELLA F.Impedance functions of pilesin layered media[J].Journal of the Engineering MechanicalDivision,ASCE,1978,104(EM3):643–661.
[18]NOVAK M,NOGAMI T,ABOUL-ELLA F.Dynamic soilreaction for plane strain case[J].Journal of the EngineeringMechanical Division,ASCE,1978,104(EM4):953–959.
[19]胡昌斌,黄晓明.成层黏弹性土中桩土耦合纵向振动时域响应研究[J].地震工程与工程振动,2006,26(4):205–211.(HU Chang-bin,HUANG Xiao-ming.A quasi-analyticalsolution to soil-pile interaction in longitudinal vibration inlayered soils considering vertical wave effect on soils[J].Earthquake Engineering and Engineering Vibration,2006,26(4):205–211.(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 De-sen,LUAN Mao-tian,YANG Qing.Review of dynamic Winkler model applied in pile-soilinteraction analyses[J].World Earthquake Engineering,2005,21(1):12–17.(in Chinese))
[21]冯世进,陈云敏,刘明振.成层土中黏弹性桩纵向振动分析及工程应用[J].中国公路学报,2004,17(2):59–63.(FENG Shi-jin,CHEN Yun-min,LIU Ming-zhen.Analysisand application in engineering on vertical vibration ofviscoelasticity piles in layered soil[J].China Journal ofHighway and Transport,2004,17(2):59–63.(in Chinese))
[22]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 Hai-dong,SHANG Shou-ping.Research on verticaldynamic response of single-pile in radically inhomogeneoussoil during the passage of Rayleigh waves[J].Journal ofVibration Engineering,2006,19(2):258–264.(in Chinese))
[23]LYSMER J,RICHART F E.Dynamic response of footing tovertical load[J].Soil Mechanics and Foundation Division.ASCE,1966,2(1):65–91.
[2]EI NAGGAR M H,WEI J Q.Experimental study of axialbehavior of tapered pile[J].Canadian Geotechnical Journal,1998,35:641–654.
[3]EI NAGGAR M H,MOHAMMED S.Evaluation of axialperformance of tapered piles from centrifuge tests[J].Canadian Geotechnical Journal,2000,37(6):1295–1308.
[4]WEI J Q.Experimental investigation of tapered piles[D].Ontario:The University of Western Ontario,1998.
[5]MOHAMMED S,EI NAGGAR M H,MONCEF N.Loadtransfer of fiber-reinforced polymer(FRP)composite taperedpiles in dense sand[J].Canadian Geotechnical Journal,2004,41(1):70–95.
[6]蒋建平,高广运,顾宝和.扩底桩、楔形桩、等直径桩对比试验研究[J].岩土工程学报,2003,26(6):764–766.(JIANG Jian-ping,GAO Guang-yun,GU Bao-he.Comparison of belled pile,tapered pile and equal-diameterpile[J].Chinese Journal of Geotechnical Engineering,2003,26(6):764–766.(in Chinese))
[7]刘杰,王忠海.楔形桩承载力实验研究[J].天津大学学报,2002,35(4):257–260.(LIU Jie,WANG Zhong-hai.Experimental study on the bearing capacity of wedge pile[J].Journal of Tianjin University,2002,35(4):257–260.(inChinese))
[8]王奎华,吴文兵,叶良,等.基于极限平衡理论的楔形桩承载力计算方法[J].建筑科学与工程学报,2009,26(4):108–113.(WANG Kui-hua,WU Wen-bing,YE Liang,et al.Calculation method of bearing capacity of tapered pile basedon limit equilibrium theory[J].Journal of Architecture andCivil Engineering,2009,26(4):108–113.(in Chinese))
[9]刘杰,何杰,闵长青.楔形刚性桩复合地基中桩的最佳楔角范围研究[J].工程力学,2009,10(增刊1):293–299.(LIU Jie,HE Jie,MIN Chang-qing.Study of the rationalwedge angle range in a composite foundation with stifftapered piles[J].Engineering Mechanics,2009,10(S1):293–299.(in Chinese))
[10]刘杰,何杰,闵长青.楔形桩与圆柱形桩复合地基承载形状对比研究[J].岩土力学,2010,31(7):2202–2206.(LIU Jie,HE Jie,MIN Chang-qing.Contrast research ofbearing behavior for composite foundation with tapered pilesand cylindrical piles[J].Rock and Soil Mechanics,2010,31(7):2202–2206.(in Chinese))
[11]刘杰,何杰,闵长青.夯实水泥土楔形桩复合地基中桩的合理楔角范围研究[J].土木工程学报,2010,43(6):122–127.(LIU Jie,HE Jie,MIN Chang-qing.Study of therational wedge angle range in a composite foundation withrammed soil-cement tapered piles[J].China CivilEngineering Journal,2010,43(6):122–127.(in Chinese))
[12]GOUGH W,RICHARDS J P G.,WILLIAMS R P.Vibrationand waves[M].New York:Halsted Press of John Wiley&Sons,1983.
[13]VAN KOTEN H,MIDDENDORP P,VAN BREDERODE P.An analysis of dissipative wave propagation in a pile[C]//IntSeminar on the Application of Stress-Wave Theory on Piles,Stockholm,1980:210–215.
[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.(WANGKui-hua,XIE Kang-he,ZENG Guo-xi.Analytical solution tovibration of finite length pile under exciting force and itsapplication[J].Chinese Journal of Geotechnical Engineering,1997,19(6):27–35.(in Chinese))
[15]王奎华,李冰河,谢康和,等.弹性支承桩受迫振动问题广义函数解及应用[J].浙江大学学报(自然科学版),1998,32(5):545–551.(WANG Kui-hua,LI Bing-he,XIE Kang-he,et al.A generalized solution to the vibration of elasticsupporting foundation pile under exciting force and itsapplication[J].Journal of Zhejiang University(NaturalScience),1998,32(5):545–551.(in Chinese))
[16]王奎华,谢康和,曾国熙.变截面阻抗桩受迫振动问题解析解及应用[J].土木工程学报,1998,31(6):56–67.(WANG Kui-hua,XIE Kang-he,ZENG Guo-xi.Ananalytical solution to force vibration of foundation pile withvariable section impedance and its application[J].China CivilEngineering Journal,1998,31(6):56–67.(in Chinese))
[17]NOVAK M,ABOUL-ELLA F.Impedance functions of pilesin layered media[J].Journal of the Engineering MechanicalDivision,ASCE,1978,104(EM3):643–661.
[18]NOVAK M,NOGAMI T,ABOUL-ELLA F.Dynamic soilreaction for plane strain case[J].Journal of the EngineeringMechanical Division,ASCE,1978,104(EM4):953–959.
[19]胡昌斌,黄晓明.成层黏弹性土中桩土耦合纵向振动时域响应研究[J].地震工程与工程振动,2006,26(4):205–211.(HU Chang-bin,HUANG Xiao-ming.A quasi-analyticalsolution to soil-pile interaction in longitudinal vibration inlayered soils considering vertical wave effect on soils[J].Earthquake Engineering and Engineering Vibration,2006,26(4):205–211.(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 De-sen,LUAN Mao-tian,YANG Qing.Review of dynamic Winkler model applied in pile-soilinteraction analyses[J].World Earthquake Engineering,2005,21(1):12–17.(in Chinese))
[21]冯世进,陈云敏,刘明振.成层土中黏弹性桩纵向振动分析及工程应用[J].中国公路学报,2004,17(2):59–63.(FENG Shi-jin,CHEN Yun-min,LIU Ming-zhen.Analysisand application in engineering on vertical vibration ofviscoelasticity piles in layered soil[J].China Journal ofHighway and Transport,2004,17(2):59–63.(in Chinese))
[22]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 Hai-dong,SHANG Shou-ping.Research on verticaldynamic response of single-pile in radically inhomogeneoussoil during the passage of Rayleigh waves[J].Journal ofVibration Engineering,2006,19(2):258–264.(in Chinese))
[23]LYSMER J,RICHART F E.Dynamic response of footing tovertical load[J].Soil Mechanics and Foundation Division.ASCE,1966,2(1):65–91.
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