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针对非饱和土中桩的水平稳态振动问题,采用三相多孔介质波动方程,考虑固、液、气三相材料间的惯性和黏性耦合效应以及基质吸力的影响,通过Helmholtz矢量分解及分离变量法解耦波动方程,并将基桩等效为能描述其剪切变形和转动惯性效应的铁摩辛柯(Timoshenko)梁模型,采用Novak三维连续介质模型对非饱和土中端承桩的稳态水平振动进行了理论推导,获得了桩顶水平频域响应解析解,讨论了饱和度对土层和桩顶阻抗的影响以及桩身位移、内力沿深度的分布规律。结果表明,随着土体饱和度的升高,土层复阻抗和桩顶动力阻抗增大,桩身位移和内力则相应地减小;饱和度,包括渗透系数在内的影响仅在土体接近准饱和时才得以发挥;频率较低时,短桩拥有较大的刚度因子。桩长越长,阻抗因子越大,而共振频率越低。当长径比超过10时,桩顶阻抗不再随长径比的增加而改变。
In order to solve the horizontal steady state vibration of piles in unsaturated soils, the wave equation of three-phase porous media is adopted. Considering the effects of inertia, viscous coupling and matrix suction between solid, liquid and gas phases, the Helmholtz vector decomposition and separation Variable method is used to decouple the wave equation and the pile is equivalent to a Timoshenko beam model that can describe the shear deformation and rotational inertia effect. Novak three-dimensional continuum model The steady-state horizontal vibration is deduced theoretically, and the analytic solution of pile top horizontal frequency response is obtained. The influence of saturation on the impedance of soil and pile top and the distribution rule of pile displacement and internal force along the depth are discussed. The results show that with the increase of soil saturation, the complex impedance of soil and the dynamic impedance of pile top increase, while the displacement and internal force of pile decrease correspondingly. The influence of saturation, including permeability coefficient, Close to quasi-saturation to be able to play; lower frequencies, the short pile has a larger stiffness factor. The longer the pile length, the larger the impedance factor, and the lower the resonance frequency. When the aspect ratio exceeds 10, the impedance at the top of the pile no longer changes with the increase of aspect ratio.