饱和地基表面基础在Rayleigh波作用下的摇摆振动分析
|
摘要
考虑地基与基础的相互作用,运用Biot波动方程理论,研究了饱和地基表面有质量的刚性圆形基础在入射Rayleigh波作用下的摇摆振动问题。将饱和地基中的总波场分解为自由波场、刚体辐射波场及刚体散射波场,从而考虑基础对Rayleigh波的散射。采用Hankel变换求解土体控制方程,结合基础摇摆振动的混合边值条件以及Rayleigh波的动力作用获得基础摇摆振动振幅的表达式。计算结果分析了泊松比、基础质量、透水条件、土体渗透系数等对基础摇摆振动的影响。研究结果表明,与弹性介质相比,饱和地基中孔隙水的存在减弱了基础的摇摆振动,其作用效果与土体渗透系数及地基表面排水条件密切相关。
Considering the interaction between soil and foundation,an investigation is put into rocking vibrations of a rigid circular foundation on the poroelastic soil excited by incident Rayleigh waves based on Biot's dynamic theory.The free field,rigid-body radiation field and rigid-body scattering field are introduced in order to consider the scattering phenomena caused by the existence of the foundation.Using the Hankel integral transforms,the governing equations of the soil are solved.Combining with the mixed boundary-value condition at the interface between the soil and the foundation,expression of the rocking dynamic amplitude of the foundation under the action of the Rayleigh waves is obtained.Influences of the Poisson ratio,the mass of foundation,the boundary drainage,the permeability of soil on rocking vibrations of the foundation are determined through numerical calculation.Computed results show that pore water in the soil has weakening effect on rocking vibrations comparing with that in elastic half-space.And the weakening effect depends upon the boundary drainage and permeability of soil.
Considering the interaction between soil and foundation,an investigation is put into rocking vibrations of a rigid circular foundation on the poroelastic soil excited by incident Rayleigh waves based on Biot's dynamic theory.The free field,rigid-body radiation field and rigid-body scattering field are introduced in order to consider the scattering phenomena caused by the existence of the foundation.Using the Hankel integral transforms,the governing equations of the soil are solved.Combining with the mixed boundary-value condition at the interface between the soil and the foundation,expression of the rocking dynamic amplitude of the foundation under the action of the Rayleigh waves is obtained.Influences of the Poisson ratio,the mass of foundation,the boundary drainage,the permeability of soil on rocking vibrations of the foundation are determined through numerical calculation.Computed results show that pore water in the soil has weakening effect on rocking vibrations comparing with that in elastic half-space.And the weakening effect depends upon the boundary drainage and permeability of soil.
引文
[1]FLITMAN L M.On the motion of a rigid strip-mass lyingon an elastic half space and excited by a seismic wave[J].Journal of Applied Mathematics and Mechanics,1962,26:1582-1604.
[2]KARASUDHI P,KEER L M,LEE S L.Vibratory motionof a body on an elastic half space[J].Journal of AppliedMechanics,1968,35:679-705.
[3]THAU S A.Radiation and scattering from a rigidinclusion in an elastic medium[J].Journal of AppliedMechanics,1967,34(2):509-511.
[4]THAU S A,UMEK A.Transient response of a buriedfoundation to antiplane shear waves[J].Journal ofApplied Mechanics,1973,40(4):1061-1066.
[5]李伟华,赵成刚,杜楠馨.软弱饱和土夹层对地铁车站地震响应的影响分析[J].岩土力学,2010,12(31):3958-3963.LI Wei-hua,ZHAO Cheng-gang,DU Nan-xin.Analysisof effects of saturated soft interlayer on seismic responsesof metro station[J].Rock and Soil Mechanics,2010,122(31):3958-3963.
[6]TAJUDDIN M.Rayleigh wave in a poroelastic half-space[J].Journal of the Acoustical Society of America,1984,75(3):682-684.
[7]夏唐代,陈龙珠,吴世明.半空间饱和土中瑞利波特性[J].水利学报,1998,2(2):47-53.XIA Tang-dai,CHEN Long-zhu,WU Shi-Ming.Charac-teristics of Rayleigh waves in a saturated half-spacesoil[J].Journal of Hydraulic Engineering,1998,2(2):47-53.
[8]夏唐代,颜可珍,孙鸣宇.饱和土层中瑞利波的传播特性[J].水利学报,2004,11(11):81-84.XIA Tang-dai,YAN Ke-zhen,SUN Ming-yu.Propagationof Rayleigh wave in saturated soil layer[J].Journal ofHydraulic Engineering,2004,11(11):81-84.
[9]刘凯欣,刘颖.横观各向同性含液饱和多孔介质中瑞利波的特性分析[J].力学学报,2003,35(1):101-104.LIU Kai-xin,LIU Ying.Characteristics of Rayleighwaves in transversely isotropic fluid-saturated porousmedia[J].Acta Mechanic Sinica,2003,35(1):101-104.
[10]陆建飞,聂卫东.饱和土中单桩在瑞利波作用下的动力响应[J].岩土工程学报,2008,30(2):225-231.LU Jian-fei,NIE Wei-dong.Dynamic response of a singlepile embedded in half-space saturated soil subjected toRayleigh waves[J].Chinese Journal of GeotechnicalEngineering,2008,30(2):225-231.
[11]CAI Y Q,DING G Y,XU C J,et al.Vertical amplitudereduction of Rayleigh waves by a row of piles in aporoelastic half-space[J].International Journal forNumerical and Analytical Methods in Geomechanics,2009,33(16):1799-1821
[12]BIOT M A.Theory of propagation of elastic waves in afluid-saturated porous solid.Ⅰ.Low frequency range[J].Journal of the Acoustial Society of America,1956,28(2):168-178.
[13]BIOT M A.Theory of propagation of elastic waves in afluid-saturated porous solid.Ⅱ.High frequency range[J].Journal of the Acoustical Society of America,1956,28(2):179-191.
[14]SNEDDON I.The use of integral transforms[M].Mcgraw-Hill:New York,1970.
[15]蔡袁强,胡秀青.饱和地基中埋置刚性圆柱基础的等效竖向动力刚度[J].岩石力学与工程学报,2008,27(2):361-367.CAI Yuan-qiang,HU Xiu-qing.Equivalent verticaldynamic stiffness for embedded rigid cylindrical found-ation in saturated soil[J].Chinese Journal of RockMechanics and Engineering,2008,27(2):361-367.
[16]MOW C C,PAO Y H.Diffraction of elastic waves anddynamic stress concentrations[M].New York:[s.n.],1973.
[17]NOBEL B.The solution of Bessel-function dual integralequations by a multiplying-fact method[J].MathematicalProceedings of the Cambrige Philosophical Society,1963,59:351-362.
[18]RICHART F E,HALL J R,WOODS R D.Vibrations ofsoils and foundations[M].New York:Prentice-Hall,1970.
[19]LUCO J E,MITA A.Response of a circular foundation ona uniform half-space to elastic waves[J].EarthquakeEngineering and Structural Dynamics,1987,15(1):105-118.
[2]KARASUDHI P,KEER L M,LEE S L.Vibratory motionof a body on an elastic half space[J].Journal of AppliedMechanics,1968,35:679-705.
[3]THAU S A.Radiation and scattering from a rigidinclusion in an elastic medium[J].Journal of AppliedMechanics,1967,34(2):509-511.
[4]THAU S A,UMEK A.Transient response of a buriedfoundation to antiplane shear waves[J].Journal ofApplied Mechanics,1973,40(4):1061-1066.
[5]李伟华,赵成刚,杜楠馨.软弱饱和土夹层对地铁车站地震响应的影响分析[J].岩土力学,2010,12(31):3958-3963.LI Wei-hua,ZHAO Cheng-gang,DU Nan-xin.Analysisof effects of saturated soft interlayer on seismic responsesof metro station[J].Rock and Soil Mechanics,2010,122(31):3958-3963.
[6]TAJUDDIN M.Rayleigh wave in a poroelastic half-space[J].Journal of the Acoustical Society of America,1984,75(3):682-684.
[7]夏唐代,陈龙珠,吴世明.半空间饱和土中瑞利波特性[J].水利学报,1998,2(2):47-53.XIA Tang-dai,CHEN Long-zhu,WU Shi-Ming.Charac-teristics of Rayleigh waves in a saturated half-spacesoil[J].Journal of Hydraulic Engineering,1998,2(2):47-53.
[8]夏唐代,颜可珍,孙鸣宇.饱和土层中瑞利波的传播特性[J].水利学报,2004,11(11):81-84.XIA Tang-dai,YAN Ke-zhen,SUN Ming-yu.Propagationof Rayleigh wave in saturated soil layer[J].Journal ofHydraulic Engineering,2004,11(11):81-84.
[9]刘凯欣,刘颖.横观各向同性含液饱和多孔介质中瑞利波的特性分析[J].力学学报,2003,35(1):101-104.LIU Kai-xin,LIU Ying.Characteristics of Rayleighwaves in transversely isotropic fluid-saturated porousmedia[J].Acta Mechanic Sinica,2003,35(1):101-104.
[10]陆建飞,聂卫东.饱和土中单桩在瑞利波作用下的动力响应[J].岩土工程学报,2008,30(2):225-231.LU Jian-fei,NIE Wei-dong.Dynamic response of a singlepile embedded in half-space saturated soil subjected toRayleigh waves[J].Chinese Journal of GeotechnicalEngineering,2008,30(2):225-231.
[11]CAI Y Q,DING G Y,XU C J,et al.Vertical amplitudereduction of Rayleigh waves by a row of piles in aporoelastic half-space[J].International Journal forNumerical and Analytical Methods in Geomechanics,2009,33(16):1799-1821
[12]BIOT M A.Theory of propagation of elastic waves in afluid-saturated porous solid.Ⅰ.Low frequency range[J].Journal of the Acoustial Society of America,1956,28(2):168-178.
[13]BIOT M A.Theory of propagation of elastic waves in afluid-saturated porous solid.Ⅱ.High frequency range[J].Journal of the Acoustical Society of America,1956,28(2):179-191.
[14]SNEDDON I.The use of integral transforms[M].Mcgraw-Hill:New York,1970.
[15]蔡袁强,胡秀青.饱和地基中埋置刚性圆柱基础的等效竖向动力刚度[J].岩石力学与工程学报,2008,27(2):361-367.CAI Yuan-qiang,HU Xiu-qing.Equivalent verticaldynamic stiffness for embedded rigid cylindrical found-ation in saturated soil[J].Chinese Journal of RockMechanics and Engineering,2008,27(2):361-367.
[16]MOW C C,PAO Y H.Diffraction of elastic waves anddynamic stress concentrations[M].New York:[s.n.],1973.
[17]NOBEL B.The solution of Bessel-function dual integralequations by a multiplying-fact method[J].MathematicalProceedings of the Cambrige Philosophical Society,1963,59:351-362.
[18]RICHART F E,HALL J R,WOODS R D.Vibrations ofsoils and foundations[M].New York:Prentice-Hall,1970.
[19]LUCO J E,MITA A.Response of a circular foundation ona uniform half-space to elastic waves[J].EarthquakeEngineering and Structural Dynamics,1987,15(1):105-118.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心