虚土桩扩散角对桩的纵向振动特性影响研究
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摘要
在桩端土单层、桩侧土成层条件下,采用锥形虚土桩假设,研究虚土桩扩散角对桩纵向振动特性的影响。首先将桩体正下方到基岩的单层土体简化成锥形虚土桩,并划分为多个薄层,采用平面应变模型对桩侧土求解得到桩(和虚土桩)剪切复刚度,然后根据桩土耦合条件,求解桩(和虚土桩)纵向振动方程,利用复刚度传递法递推得到虚土桩桩顶的复刚度,并将其作为桩端土的实际支承刚度,进一步得到桩顶频域和时域响应表达式,最后分析虚土桩扩散角对桩动力特性影响的规律性,为虚土桩法研究和应用提供理论依据。
Based on the hypothesis of fictitious soil pile,the influence of cone angle on dynamic response is presented.The soil around pile is assumed to be layered while the soil under pile is assumed to be single.The conical soil pile,a simlified model of soil layer under the pile,is divided into many thin slices.Then the complex circumferential shear stiffness of pile and fictitious pile is obtained by plane strain assumption.The vertical vibration equation can be solved with the boundary condition between soil and pile.By means of complex stiffness transfer method,the pile response in frequency and time domain is obtained and is used as real bearing stiffness of soil.Finally,the effects of cone angle on the dynamic response of pile is analized,which provides theoretical basis for further study and application of fictitious soil pile model.
Based on the hypothesis of fictitious soil pile,the influence of cone angle on dynamic response is presented.The soil around pile is assumed to be layered while the soil under pile is assumed to be single.The conical soil pile,a simlified model of soil layer under the pile,is divided into many thin slices.Then the complex circumferential shear stiffness of pile and fictitious pile is obtained by plane strain assumption.The vertical vibration equation can be solved with the boundary condition between soil and pile.By means of complex stiffness transfer method,the pile response in frequency and time domain is obtained and is used as real bearing stiffness of soil.Finally,the effects of cone angle on the dynamic response of pile is analized,which provides theoretical basis for further study and application of fictitious soil pile model.
引文
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[2]胡昌斌,黄晓明.成层粘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 Changbin,Huang Xiaoming.A quasi-analytical solution to soil-pile interaction in longitudinal vibration in layered soils considering vertical wave effect on soils[J].Earthquake Engineering and Engineering Vibration,2006,26(4):205―211.(in Chinese)
[3]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 applied in pile-soil interaction analyses[J].World Earthquake Engineering,2005,21(1):12―17.(in Chinese)
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[7]燕彬,黄义.群桩刚性承台竖向动阻抗的简化计算[J].岩土工程学报,2004,26(5):465―468.Yan Bin,Huang Yi.Simple method for calculating vertical dynamic impedance of rigidly-capped pile groups[J].Chinese Journal of Geotechnical Engineering,2004,26(5):465―468.(in Chinese)
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[9]栾茂田,孔德森,杨庆,韩丽娟.层状土中单桩竖向简谐动力响应简化解析方法[J].岩土力学,2005,26(3):375―380.Luan Maotian,Kong Desen,Yang Qing,Han Lijuan.Simplified analytic method of vertical harmonic response of single pile embedded in layered soil[J].Rock and Soil Mechanics,2005,26(3):375―380.(in Chinese)
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[11]Cai Yuanqiang,Chen Gang,Xu Changjie,Wu Dazhi.Torsional response of pile embedded in a poroelastic medium[J].Soil Dynamics and Earthquake Engineering,2006,26:1143―1148.
[12]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,2006,26:626―636.
[13]Wang Guocai,Ge Wei,Pan Xiaodong,Wang Zhe.Torsional vibrations of single piles embedded in saturated medium[J].Computers and Geotechnics,2008,35:11―21.
[14]彭吉五.考虑基岩埋置深度影响时单桩沉降特性研究[D].杭州:浙江大学,2007.Peng Jiwu.Research on the settlement of single pile considering the effect of embedded depth for bedrock[D].Hangzhou:Zhejiang University,2007.(in Chinese)
[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 Jiaxi.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 Dongying.Study on pile vertical vibration in inhomogeneous soil[D].Hangzhou:Zhejiang University,2009.(in Chinese)
[17]Novak M.Dynamic stiffness and damping of piles[J].Canadian Geotechnical Journal,1974,11(4):574―598.
[18]Novak M,Nogami T,Aboul-ella F.Dynamic soil reaction for plane strain case[J].Journal of the Engineering Mechanical Division,ASCE,1978,104(EM4):953―959.
[2]胡昌斌,黄晓明.成层粘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 Changbin,Huang Xiaoming.A quasi-analytical solution to soil-pile interaction in longitudinal vibration in layered soils considering vertical wave effect on soils[J].Earthquake Engineering and Engineering Vibration,2006,26(4):205―211.(in Chinese)
[3]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 applied in pile-soil interaction analyses[J].World Earthquake Engineering,2005,21(1):12―17.(in Chinese)
[4]Militano G,Rajapakse R K N D.Dynamic response of a pile in a multi-layered soil to transient torsional and axial loading[J].Geotechnique,1999,49(1):91―109.
[5]Gazetas G,Makris N.Dynamic pile-soil-pile interaction.Part I:analysis of axial vibration[J].Earthquake Engineering and Structural Dynamics,1991,20(1):115―132.
[6]李强,王奎华.成层饱和土中桩纵向振动特性研究及应用[J].工程力学,2007,24(10):144―149.Li Qiang,Wang Kuihua.A study on longitudinal pile vibration in saturated layered soil and its application[J].Engineering Mechanics,2007,24(10):144―149.(in Chinese)
[7]燕彬,黄义.群桩刚性承台竖向动阻抗的简化计算[J].岩土工程学报,2004,26(5):465―468.Yan Bin,Huang Yi.Simple method for calculating vertical dynamic impedance of rigidly-capped pile groups[J].Chinese Journal of Geotechnical Engineering,2004,26(5):465―468.(in Chinese)
[8]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)
[9]栾茂田,孔德森,杨庆,韩丽娟.层状土中单桩竖向简谐动力响应简化解析方法[J].岩土力学,2005,26(3):375―380.Luan Maotian,Kong Desen,Yang Qing,Han Lijuan.Simplified analytic method of vertical harmonic response of single pile embedded in layered soil[J].Rock and Soil Mechanics,2005,26(3):375―380.(in Chinese)
[10]Muki R,Sternberg E.Electrostatic load transfer to a half space from a partially embedded axially loaded rod[J].Solids and Struct,1970,6:69―90.
[11]Cai Yuanqiang,Chen Gang,Xu Changjie,Wu Dazhi.Torsional response of pile embedded in a poroelastic medium[J].Soil Dynamics and Earthquake Engineering,2006,26:1143―1148.
[12]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,2006,26:626―636.
[13]Wang Guocai,Ge Wei,Pan Xiaodong,Wang Zhe.Torsional vibrations of single piles embedded in saturated medium[J].Computers and Geotechnics,2008,35:11―21.
[14]彭吉五.考虑基岩埋置深度影响时单桩沉降特性研究[D].杭州:浙江大学,2007.Peng Jiwu.Research on the settlement of single pile considering the effect of embedded depth for bedrock[D].Hangzhou:Zhejiang University,2007.(in Chinese)
[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 Jiaxi.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 Dongying.Study on pile vertical vibration in inhomogeneous soil[D].Hangzhou:Zhejiang University,2009.(in Chinese)
[17]Novak M.Dynamic stiffness and damping of piles[J].Canadian Geotechnical Journal,1974,11(4):574―598.
[18]Novak M,Nogami T,Aboul-ella F.Dynamic soil reaction for plane strain case[J].Journal of the Engineering Mechanical Division,ASCE,1978,104(EM4):953―959.
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