非饱和土中端承桩水平振动特性研究

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。

Horizontal vibration of an end-bearing pile in unsaturated soil

Up to now horizontal vibration response of a single pile in unsaturated soil is analyzed theoretically. The unsaturated soil surrounding pile is described by three-phase poro-elastic theory, which takes into account the viscous and inertial coupling between solid skeleton and pore fluids as well as the matrix suction, while the pile embedded in unsaturated soil is end bearing and treated as a Timoshenko beam model to describe the shear deformation and rotational inertia effects. The Helmholtz decomposition and variable separation method are firstly adopted to decouple the governing equations of the unsaturated soil. And then a rigorous mathematical formulation of the pile-head frequency–response function is deduced by virtue of the three-dimensional continuum model proposed by Novak and the compatibility between the pile and soil. The influences of degree of saturation on the impedances of pile and soil together with the distribution of displacement and internal force along the pile are discussed in detail. Results indicate that both the complex impedance of soil and the dynamic impedance of pile top increase with the increasing degree of saturation of soil, while the deformation and the internal force of pile are reduced. The contribution of pore water to dynamic behavior is made only when the soil is close to the saturated condition. At low frequencies, short pile has a large stiffness factor. A longer pile will lead to a higher damping factor, but a low resonance frequency. The impedance at the top of pile would be approximately invariant as the pile’s slenderness ratio exceeds 10.