考虑波动效应的SH简谐地震波作用下单桩水平振动研究
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摘要
借助于土体的一维波动模型求解了SH简谐地震波作用下土层的水平振动,从三维轴对模型出发考虑桩周土的水平波动效应,通过引入势函数并运用分离变量法在考虑桩–土相互作用的情况下求解了SH简谐地震波作用下由于桩土相互作用引起的土层的径向位移、水平位移以及土体对桩基的水平作用力,并在此基础上建立了SH简谐地震波作用下桩基的水平振动方程,借助于三角函数的正交性和桩–土接触面处的连续条件求得了桩基的水平位移。借助于放大因子的概念研究了SH简谐地震波对桩顶水平位移的影响。研究表明:SH简谐地震波作用下桩基的动力响应存在有共振现象;放大因子随频率的变化曲线存在3个峰值,前两个峰值相对较大;当桩土模量比较大时桩土模量比对放大因子几乎没有影响。
The lateral vibration of the soil under SH harmonic seismic waves is solved by one-dimensional model of wave motion.On the basis of three-dimensional soil model and taking consideration of wave effect of soil,the radial displacement and horizontal displacement caused by pile-soil interaction and the lateral soil force on the pile are obtained by means of the potential functions and variable separation method,and the lateral dynamic equation of the pile is established by considering the orthogonality of trigonometric function and the continuous conditions at the soil-pile contact surfaces.The influence of the SH harmonic seismic waves on the horizontal displacement of the pile head is investigated by the concept of magnification factor.The results indicate that the dynamic response of the pile under SH harmonic seismic waves has resonance.There are three peaks of the curves of amplification factor versus frequency,and the first two peaks are relatively larger.The pile-soil modulus ration has little effect on the amplification factor when the pile-soil modulus ration is larger.
The lateral vibration of the soil under SH harmonic seismic waves is solved by one-dimensional model of wave motion.On the basis of three-dimensional soil model and taking consideration of wave effect of soil,the radial displacement and horizontal displacement caused by pile-soil interaction and the lateral soil force on the pile are obtained by means of the potential functions and variable separation method,and the lateral dynamic equation of the pile is established by considering the orthogonality of trigonometric function and the continuous conditions at the soil-pile contact surfaces.The influence of the SH harmonic seismic waves on the horizontal displacement of the pile head is investigated by the concept of magnification factor.The results indicate that the dynamic response of the pile under SH harmonic seismic waves has resonance.There are three peaks of the curves of amplification factor versus frequency,and the first two peaks are relatively larger.The pile-soil modulus ration has little effect on the amplification factor when the pile-soil modulus ration is larger.
引文
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[2]TOKIMATSU K,MIZUNO H,KAKURAI M.Buildingdamage associated with geotechnical problems[J].Soils andFoundations,1996(S1):219–234.
[3]FINN W D L,GOHL W B.Response of model pile groups tostrong shaking[C]//Proceedings of the Conference on PilesUnder Dynamic Loads.New York,1992:27–55.
[4]KAYNIA A M,NOVAK M.Response of pile foundations toRayleigh waves and obliquely body wave[J].EarthquakeEngineering and Structural Dynamics,1992,21:303–318.
[5]MAKRIS N.Soil-pile interaction during the passage of Rayleighwaves.An analytical solution[J].Earthquake Engineering andStructural Dynamics,1994,23(2):153–167.
[6]王立忠,冯永正,柯瀚,等.瑞利波作用下成层地基中单桩的横向振动分析[J].振动工程学报,2001,14(2):205–209.(WANG Li-zhong,FENG Yong-zheng,KE Han,et al.Lateral dynamic response of single pile in multiple layers soilduring the passage of Rayleigh waves[J].Journal of VibrationEngineering,2001,14(2):205–209.(in Chinese))
[7]王海东,尚守平.瑞利波作用下径向非均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 inhomogeneous soilduring the passage of Rayleigh waves[J].Journal of VibrationEngineering,2006,19(2):258–264.(in Chinese))
[8]王海东,尚守平.瑞利波作用下考虑桩土相互作用的单桩竖向动力响应计算研究[J].工程力学,2006,23(8):74–78.(WANG Hai-dong,SHANG Shou-ping.Computationalresearch on vertical dynamic response of single-pile consideringpile-soil interaction during passage of Rayleigh waves[J].Engineering Mechanics,2006,23(8):74–78.(in Chinese))
[9]刘林超,闫启方,杨骁.SH简谐波作用下桩土横向动力相互作用解析分析[J].公路交通科技,2010,27(10):25–28.(LIU Lin-chao,YAN Qi-fang,YANG Xiao.Analysis onpile-soil lateral dynamic interaction under SH harmonic waveexcitation[J].Journal of Highway and Transportation Researchand Development,2010,27(10):25–28.(in Chinese))
[10]刘林超,杨骁.基于基于严格平面应变模型的土中群桩水平振动研究[J].工程力学,2010,42(7):168–174.(LIULin-chao,YANG Xiao.Lateral vibration of pile groups insoil based on plane strain model[J].Engineering Mechanics,2010,42(7):168–174.(in Chinese))
[11]余俊,尚守平,李忠,等.饱和土中端承桩水平振动动力响应分析[J].岩土工程学报,2009,31(3):408–415.(YUJun,SHANG Shou-ping,LI Zhong,et al.Dynamicalcharacteristics of an end bearing pile embedded in saturated soilunder horizontal vibration[J].Chinese Journal of GeotechnicalEngineering,2009,31(3):408–415.(in Chinese))
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