考虑土体三维波动效应时弹性支承桩的振动理论及其应用

Theory of vibration of pile on elastic foundation considering 3D wave effect of soil and its applications

从三维轴对称土体模型出发,同时考虑土体竖向和径向位移,对弹性支承桩在垂直谐和激振力作用下与土的耦合振动特性进行了分析。假定桩为竖直弹性等截面体,土为线性粘弹性体,其材料阻尼为滞回阻尼。首先通过引入势函数对土体位移进行分解,从而将土体动力平衡方程解耦,求解得到了土层的振动模态形式,然后利用桩土接触面上力平衡和位移连续条件来考虑桩土耦合作用,求解桩的动力平衡方程,得到了桩顶的频域响应解析解、复刚度和速度导纳,利用卷积定理和傅立叶逆变换,求得了半正弦脉冲激振力作用下桩顶速度时域响应半解析解。利用所得解对桩的振动特性进行了无量纲参数分析,得到了许多新的结论。

Modeling soil as a 3D axisymmetric continuum and taking its radial and vertical displacement into account, the interaction between a soil layer and a pile with elastic bottom boundary undergoing vertical harmonic load is theoretically investigated. The pile is assumed to be vertical, elastic and of uniform cross-section, and the soil is considered as a linear visco-elastic layer with hysteretic type damping. With the aid of two potentials, the displacement of the soil is decomposed and then the dynamic equilibrium equation of soil layer is uncoupled and solved first. Thus the vibration modes of the soil layer are obtained and used to analyse the response on pile. By considering the interaction between the soil layer and the pile with boundary condition of continuity of displacement and equilibrium of force at their interface, the dynamic equilibrium equation of pile is solved and an analytical solution for the response on pile in frequency domain is obtained, which is used to define the complex stiffness and mobility at the level of the pile head. Based on the convolution theorem and inverse Fourier transform, a semi-analytical solution of velocity response in time-domain subjected to a semi-sine exciting force is given. A parametric study of the effect of these governing dimensionless parameters is conducted to illustrate the behavior of soil-pile interaction. Some new conclusions are drawn.