双层地基中考虑桩体剪切变形的单桩水平振动解析解
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摘要
基于动力Winkler模型(BDWF)对双层粘弹性地基中单桩的水平动力响应进行求解。采用与频率相关的刚度系数和阻尼系数来模拟动反力,桩体则被简化为Timoshenko梁,同时考虑了其弯曲和剪切变形,得到了单桩水平振动更为精确的解析解。在此基础上,研究了桩土模量比、桩体长径比、地基成层性以及激振频率对桩基动力响应的影响。最后,在给定桩土参数的情况下,把所得的同时考虑桩体弯曲和剪切变形的解析解与前人只考虑弯曲变形的解进行了比较,结果表明:忽略桩体水平振动时的剪切变形会带来较大的误差,用笔者所给出的更为精确的解析理论才能给出满意的解答;均匀地基中所得的界限桩长并不适用于双层地基,双层地基中剪切变形的影响规律及其因素需要深入研究。
The beam-on-dynamic-Winkler-foundation (BDWF) model is utilized to determine the horizontal dynamic response of a single pile in double-layer viscoelastic soils. Based on frequency-dependent 憇prings?and 慸ashpots?the pile is modeled as a Timoshenko beam considering both bending and shearing and a more rigorous analytical solution of horizontal vibration for a single pile is developed. On the basis of the solution developed here,the influence of many parameters on the dynamic response of pile,such as the ratio of the Young抯 modulus of the pile to that of the soil,the ratio of pile length to its diameter,the variation of soil properties and the frequency,is studied. Furthermore,a comparison is also made between the theory here and that based on Euler beam model in two-layered soils. It is found that the theory based on Euler beam gives more errors without considering the parameters given here. Thus,in the analysis on horizontal vibration of pile in layered soils,the more rigorous theory presented herein should be used,otherwise more errors can be brought forward to the analysis result.
The beam-on-dynamic-Winkler-foundation (BDWF) model is utilized to determine the horizontal dynamic response of a single pile in double-layer viscoelastic soils. Based on frequency-dependent 憇prings?and 慸ashpots?the pile is modeled as a Timoshenko beam considering both bending and shearing and a more rigorous analytical solution of horizontal vibration for a single pile is developed. On the basis of the solution developed here,the influence of many parameters on the dynamic response of pile,such as the ratio of the Young抯 modulus of the pile to that of the soil,the ratio of pile length to its diameter,the variation of soil properties and the frequency,is studied. Furthermore,a comparison is also made between the theory here and that based on Euler beam model in two-layered soils. It is found that the theory based on Euler beam gives more errors without considering the parameters given here. Thus,in the analysis on horizontal vibration of pile in layered soils,the more rigorous theory presented herein should be used,otherwise more errors can be brought forward to the analysis result.
引文
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7TakemiyaH,YamadaY.Layered soil-pile-structure dynamic interaction[J].EarthquakeEngineering andStructuralDynamics,1981,9(5):437～457
8韩英才,NovakM.水平荷载作用下单桩的动力分析[J].地震工程与工程振动,1989,9(2):97～106
9赵振东,傅铁铭,土歧宪三.桩头侧向集中荷载作用下桩-土系统的非线性动力性能分析[J].地震工程与工程振动,1997,17(3):100～109
10MylonakisG,GazetasG.Lateral vibration and internal forces of grouped piles in layered soils[J].Journal ofGeotechnical andGeoenvironmentalEngineering,1999,125(1):16～25
11MakrisN,GazetasG.Dynamic pile-soil-pile interaction,partII:lateral and seismic response[J].EarthquakeEngineering andStructuralDynamics,1992,21(2):145～162
12胡安峰,谢康和,王奎华.粘弹性地基中有限长桩横向受迫振动问题解析解[J].岩土力学,2003,24(1):25～29
13胡安峰,谢康和,应宏伟等.粘弹性地基中考虑桩体剪切变形的单桩水平振动解析理论[J].岩石力学与工程学报,2004,23(9):1515～1520
14TimoshenkoS P.On the correction for shear of the differential equation for transverse vibration of prismatic bars[J].PhilosophicalMagazine,1921,41:744～754
15王光远.建筑结构的振动[M].北京:科学出版社,1978
16胡安峰,谢康和,肖志荣.水平荷载下单桩动力反应分析[J].浙江大学学报(工学版),2003,37(4):420～425
2NogamiT,NovakM.Resistance of soil to a horizontally vibrating pile[J].EarthquakeEngineering andStructuralDynamics,1977,5(3):249～261
3NogamiT,NovakM.Coefficient of soil reaction to pile vibration[J].Journal ofGeotechnicalEngineering,1980,106(5):565～569
4NovakM,Aboul-ellaF.Impedances functions of piles in layered media[J].Journal ofEngineeringMechanics,1978,104(3):643～661
5NovakM,NogamiT.Soil-pile interaction in horizontal vibration[J].EarthquakeEngineering andStructuralDynamics,1977,5(3):263～281
6NovakM,NogamiT,Aboul-ellaF.Dynamic soil reactions for plane strain case[J].Journal ofEngineeringMechanics,1978,104(4):953～959
7TakemiyaH,YamadaY.Layered soil-pile-structure dynamic interaction[J].EarthquakeEngineering andStructuralDynamics,1981,9(5):437～457
8韩英才,NovakM.水平荷载作用下单桩的动力分析[J].地震工程与工程振动,1989,9(2):97～106
9赵振东,傅铁铭,土歧宪三.桩头侧向集中荷载作用下桩-土系统的非线性动力性能分析[J].地震工程与工程振动,1997,17(3):100～109
10MylonakisG,GazetasG.Lateral vibration and internal forces of grouped piles in layered soils[J].Journal ofGeotechnical andGeoenvironmentalEngineering,1999,125(1):16～25
11MakrisN,GazetasG.Dynamic pile-soil-pile interaction,partII:lateral and seismic response[J].EarthquakeEngineering andStructuralDynamics,1992,21(2):145～162
12胡安峰,谢康和,王奎华.粘弹性地基中有限长桩横向受迫振动问题解析解[J].岩土力学,2003,24(1):25～29
13胡安峰,谢康和,应宏伟等.粘弹性地基中考虑桩体剪切变形的单桩水平振动解析理论[J].岩石力学与工程学报,2004,23(9):1515～1520
14TimoshenkoS P.On the correction for shear of the differential equation for transverse vibration of prismatic bars[J].PhilosophicalMagazine,1921,41:744～754
15王光远.建筑结构的振动[M].北京:科学出版社,1978
16胡安峰,谢康和,肖志荣.水平荷载下单桩动力反应分析[J].浙江大学学报(工学版),2003,37(4):420～425
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