成层土中基于虚土桩模型的桩基纵向振动响应
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摘要
基于虚土桩模型,对成层广义Voigt地基中桩基纵向振动响应进行研究。将桩截面面积范围内有限层桩端土模拟为与桩完全接触的虚土桩,桩侧土采用广义Voigt模型,结合Laplace变换求得了瞬态半正弦脉冲荷载作用下桩顶频域响应的解析解及时域响应的半解析解;同时采用参数研究方法讨论了单层桩端土和双层桩端土情况下,土层参数对桩顶振动响应的影响,并将虚土桩模型与其他桩端土支承模型进行了对比;最后将理论结果与实际工程桩实测曲线进行了拟合对比。结果表明:该虚土桩模型较为合理,能够较真实地反映桩土相互作用机理。
Based on fictitious soil pile model,the longitudinal dynamic response to the pile under axial dynamic loading in layered general Voigt foundation was presented.The finite soil layers under the pile were modeled as fictitious soil pile in the range of cross-section area with the pile and the surrounding layered soils which were described with general Voigt model.By means of Laplace transform,the analytical solutions were obtained for the vertical dynamic response in the frequency domain and the relevant semi-analytical solutions in the time domain at condition of transient half cycle sine wave shaped on the pile top.Subsequently,the influence of parameters of pile end soil on the dynamic response at the pile top was investigated through parametric study method.Fictitious soil pile model and other pile end soil supporting model were compared.Theoretical result and field measurement curves of pile were fitted and compared.It has verified rationality of fictitious soil pile.
Based on fictitious soil pile model,the longitudinal dynamic response to the pile under axial dynamic loading in layered general Voigt foundation was presented.The finite soil layers under the pile were modeled as fictitious soil pile in the range of cross-section area with the pile and the surrounding layered soils which were described with general Voigt model.By means of Laplace transform,the analytical solutions were obtained for the vertical dynamic response in the frequency domain and the relevant semi-analytical solutions in the time domain at condition of transient half cycle sine wave shaped on the pile top.Subsequently,the influence of parameters of pile end soil on the dynamic response at the pile top was investigated through parametric study method.Fictitious soil pile model and other pile end soil supporting model were compared.Theoretical result and field measurement curves of pile were fitted and compared.It has verified rationality of fictitious soil pile.
引文
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[2]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 Kui-hua,XIE Kang-he,ZENG Guo-xi.Ana-lytical Solution to Vibration of Finite Length Pile Un-der Exciting Force and Its Application[J].ChineseJournal of Geotechnical Engineering,1997,19(6):27-35.
[3]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 onVertical Dynamic Response of Single-pile in RadiallyInhomogeneous Soil During the Passage of RayleighWaves[J].Journal of Vibration Engineering,2006,19(2):258-264.
[4]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):3190-3197.HU Chang-bin,ZHANG Tao.Time Domain TorsionalResponse of Dynamically Loaded Pile in HystereticType Damping Soil Layer[J].Chinese Journal of RockMechanics and Engineering,2006,25(S1):3190-3197.
[5]NOGAMI T,KONAGAI K.Time Domain Axial Re-sponse of Dynamically Loaded Single Piles[J].Journalof Engineering Mechanics,1986,112(11):1241-1252.
[6]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 Chang-bin,HUANG Xiao-ming.A Quasi-analyti-cal Solution to Soil-pile Interaction in LongitudinalVibration in Layered Soils Considering Vertical WaveEffect on Soils[J].Earthquake Engineering and Engi-neering Vibration,2006,26(4):205-211.
[7]孔德森,栾茂田,杨庆.桩土相互作用分析中的动力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.Re-view of Dynamic Winkler Model Applied in Pile-soilInteraction Analyses[J].World Earthquake Engineer-ing,2005,21(1):12-17.
[8]王奎华,应宏伟.广义Voigt土模型条件下桩的纵向振动响应与应用[J].固体力学学报,2003,24(3):293-303.WANG Kui-hua,YING Hong-wei.Vibration of Inho-mogeneous Pile Embedded in Layered Soils with Gen-eral Voigt Models[J].Acta Mechanica Solida Sinica,2003,24(3):293-303.
[9]冯世进,陈云敏,刘明振.成层土中粘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.A-nalysis and Application in Engineering on Vertical Vi-bration of Viscoelasticity Piles in Layered Soil[J].China Journal of Highway and Transport,2004,17(2):59-63.
[10]ZENG X,RAJAPAKSE R K N D.Dynamic AxialLoad Transfer from Elastic Bar to Poroelastic Medi-um[J].Journal of Engineering Mechanics,1999,125(9):1048-1055.
[11]MUKI R,STERNBERG E.Electrostatic Load-trans-fer to a Half-space from a Partially Embedded AxiallyLoaded Rod[J].International Journal of Solids andStructures,1970,6(1):69-90.
[12]MILITANO G,RAJAPAKSE R K N D.Dynamic Re-sponse of a Pile in a Multi-layered Soil to TransientTorsional and Axial Loading[J].Geotechnique,1999,49(1):91-109.
[13]CAI Y Q,CHEN G,XU C J,et al.Torsional Re-sponse of Pile Embedded in a Poroelastic Medium[J].Soil Dynamics and Earthquake Engineering,2006,26(12):1143-1148.
[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 Ji-wu.Research on the Settlement of SinglePile Considering the Effect of Embedded Depth forBedrock[D].Hangzhou:Zhejiang University,2007.
[15]陈嘉熹.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 A-nalysis on Method of Virtual Pile of Soil[D].Hang-zhou:Zhejiang University,2008.
[16]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):2021-2028.YANG Dong-ying,WANG Kui-hua.Vertical Vibra-tion of Pile Based on Fictitious Soil-pile Model in In-homogeneous Soil[J].Journal of Zhejiang Universi-ty:Engineering Science,2010,44(10):2021-2028.
[17]NOVAK M,ABOUL-ELLA F,NOGAMI T.DynamicSoil Reactions for Plane Strain Case[J].Journal of theEngineering Mechanics Division,1978,104(4):953-959.
[18]JGJ94—2008,建筑桩基技术规范[S].JGJ 94—2008,Technical Code for Building Pile Foun-dations[S].
[19]景胜.嵌岩桩桩底低应变反射波曲线特征及实例分析[J].岩土工程界,2008,11(2):65-66.JING Sheng.Low Strain Reflective Wave Curves ofInserted Pile Bottom in Pile Foundation Checking Sig-nals[J].Geotechnical Engineering World,2008,11(2):65-66.
[2]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 Kui-hua,XIE Kang-he,ZENG Guo-xi.Ana-lytical Solution to Vibration of Finite Length Pile Un-der Exciting Force and Its Application[J].ChineseJournal of Geotechnical Engineering,1997,19(6):27-35.
[3]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 onVertical Dynamic Response of Single-pile in RadiallyInhomogeneous Soil During the Passage of RayleighWaves[J].Journal of Vibration Engineering,2006,19(2):258-264.
[4]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):3190-3197.HU Chang-bin,ZHANG Tao.Time Domain TorsionalResponse of Dynamically Loaded Pile in HystereticType Damping Soil Layer[J].Chinese Journal of RockMechanics and Engineering,2006,25(S1):3190-3197.
[5]NOGAMI T,KONAGAI K.Time Domain Axial Re-sponse of Dynamically Loaded Single Piles[J].Journalof Engineering Mechanics,1986,112(11):1241-1252.
[6]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 Chang-bin,HUANG Xiao-ming.A Quasi-analyti-cal Solution to Soil-pile Interaction in LongitudinalVibration in Layered Soils Considering Vertical WaveEffect on Soils[J].Earthquake Engineering and Engi-neering Vibration,2006,26(4):205-211.
[7]孔德森,栾茂田,杨庆.桩土相互作用分析中的动力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.Re-view of Dynamic Winkler Model Applied in Pile-soilInteraction Analyses[J].World Earthquake Engineer-ing,2005,21(1):12-17.
[8]王奎华,应宏伟.广义Voigt土模型条件下桩的纵向振动响应与应用[J].固体力学学报,2003,24(3):293-303.WANG Kui-hua,YING Hong-wei.Vibration of Inho-mogeneous Pile Embedded in Layered Soils with Gen-eral Voigt Models[J].Acta Mechanica Solida Sinica,2003,24(3):293-303.
[9]冯世进,陈云敏,刘明振.成层土中粘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.A-nalysis and Application in Engineering on Vertical Vi-bration of Viscoelasticity Piles in Layered Soil[J].China Journal of Highway and Transport,2004,17(2):59-63.
[10]ZENG X,RAJAPAKSE R K N D.Dynamic AxialLoad Transfer from Elastic Bar to Poroelastic Medi-um[J].Journal of Engineering Mechanics,1999,125(9):1048-1055.
[11]MUKI R,STERNBERG E.Electrostatic Load-trans-fer to a Half-space from a Partially Embedded AxiallyLoaded Rod[J].International Journal of Solids andStructures,1970,6(1):69-90.
[12]MILITANO G,RAJAPAKSE R K N D.Dynamic Re-sponse of a Pile in a Multi-layered Soil to TransientTorsional and Axial Loading[J].Geotechnique,1999,49(1):91-109.
[13]CAI Y Q,CHEN G,XU C J,et al.Torsional Re-sponse of Pile Embedded in a Poroelastic Medium[J].Soil Dynamics and Earthquake Engineering,2006,26(12):1143-1148.
[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 Ji-wu.Research on the Settlement of SinglePile Considering the Effect of Embedded Depth forBedrock[D].Hangzhou:Zhejiang University,2007.
[15]陈嘉熹.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 A-nalysis on Method of Virtual Pile of Soil[D].Hang-zhou:Zhejiang University,2008.
[16]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):2021-2028.YANG Dong-ying,WANG Kui-hua.Vertical Vibra-tion of Pile Based on Fictitious Soil-pile Model in In-homogeneous Soil[J].Journal of Zhejiang Universi-ty:Engineering Science,2010,44(10):2021-2028.
[17]NOVAK M,ABOUL-ELLA F,NOGAMI T.DynamicSoil Reactions for Plane Strain Case[J].Journal of theEngineering Mechanics Division,1978,104(4):953-959.
[18]JGJ94—2008,建筑桩基技术规范[S].JGJ 94—2008,Technical Code for Building Pile Foun-dations[S].
[19]景胜.嵌岩桩桩底低应变反射波曲线特征及实例分析[J].岩土工程界,2008,11(2):65-66.JING Sheng.Low Strain Reflective Wave Curves ofInserted Pile Bottom in Pile Foundation Checking Sig-nals[J].Geotechnical Engineering World,2008,11(2):65-66.
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