非轴对称荷载下考虑流体流速的饱和土稳态动力响应
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摘要
由于饱和土中流固耦合,饱和土的动力问题不但要考虑土骨架的运动,而且还要考虑流体的运动.对此,不忽略流体相对于土骨架运动的惯性项,应用Hankel积分变换方法,对Biot波动方程逐次解耦后直接求解得通解;根据通解和半空间内部或表面作用水平力时的边界条件和作用面上的连续条件,求得边值问题的解;对边值问题的解进行相应的Hankel逆变换,就可求得应力、应变、位移、孔压等.最后给出了Hankel逆变换的数值方法.
The steady dynamic response of saturated soil was studied by means of Hankel transform. The liquid's inertia is considered, i.e. there is not any hypothesis. By using Hankel integral transform method, the solution of horizontal harmonic force applied to the interior or the surface of saturated soil is obtained. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above-mentioned general solution, the boundary conditions of the surface of half-space and the continuous conditions at the plane of horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the stress and the displacement of harmonic horizontal force are obtainable. In the end, the numerical method of inversion of Hankel transform was given.
The steady dynamic response of saturated soil was studied by means of Hankel transform. The liquid's inertia is considered, i.e. there is not any hypothesis. By using Hankel integral transform method, the solution of horizontal harmonic force applied to the interior or the surface of saturated soil is obtained. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above-mentioned general solution, the boundary conditions of the surface of half-space and the continuous conditions at the plane of horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the stress and the displacement of harmonic horizontal force are obtainable. In the end, the numerical method of inversion of Hankel transform was given.
引文
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[2] PaulS.Onthedisplacementsproducedinporouselastichalf-spacebyanimpulsivelineload(no-dissi-pativecase)[J].PureApplGeophys,1976,114(5):605-614.
[3] ChenJ.TimedomainfundamentalsolutiontoBiot'scompleteequationofdynamicporoelasticity.PartI:Two-dimensionalsolution[J].IntJSolidStruct,1994,31:1447-1490.
[4] 杨 俊,吴世明,陈云敏.弹性层和饱和半空间体系稳定动力响应[J].土木工程学报,1997,30(3):39-47.YANGJun,WUShi-ming,CHENYun-min.Steadystateresponseofelasticsoillayerandsaturatedlay-eredhalf-space[J].ChinaCivilEngineeringJour-nal,1997,30(3):39-47.
[5] 张引科,黄 义.弹性饱和多孔介质在非对称荷载下的稳态动力响应[J].土木工程学报,2002,35(3):41-45.ZHANGYin-ke,HUANGYi.Steadydynamicre-sponseofelasticsaturatedporousmediumundernonoatisymmetricalload[J].ChinaCivilEngineeringJournal,2002,35(3):41-45.
[6] 陆建飞,王建华,沈为平.半空间饱和土作用水平力的格林函数[J].地震学报,2001,23(2):185-191.LUJian-fei,WANGJian-hua,SHENWei-ping.Thegreen'sfunctionoftheharmonichorizontalforceappliedtotheinteriorofthesaturatedhalf-space[J].ActaSeismologicaSinica,2001,23(2):185-191.
[7] ZienkiewiczOC,ChangCT,BettessP.Drained,undrained,consolidatinganddynamicbehavioras-sumptionsinsolid[J].Geotech,1980,30(3):385-395.
[8] 金 波.多孔饱和半空间上弹性圆板垂直振动的积分方程[J].力学学报,2000,(1):78-85.JINBo.IntegralEquationsofverticalvibrationofanelasticcircularplateonafluid-saturatedporoelastichalfspace[J].ActaMechanicaSinica,2000,(1):78-85.
[9] ZengX,RajapakseRKND.Verticalvibrationsofarigiddiskembeddedinaporelasticmedium[J].IntJNumerAnalMechGeomech,1999,23:2075-2095.
[10] SneddonIN.Fouriertransforms[M].NewYork:McGraw-Hillv,1951.
[11] MukiR.Asymmetricproblemsofthetheoryofelas-ticityforasemi-infinitesolidandathickplate[A].ProgressinSolidMechanicsVol.1[C].NewYork:NorthHolland,1960.
[12] 陆建飞.饱和土中的桩与土共同作用问题研究[D].上海:上海交通大学建筑工程与力学学院,2000.
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