考虑土体三维波动效应时黏性阻尼土中桩的纵向振动特性及其应用研究

THEORY ON LONGITUDINAL VIBRATION OF PILE IN VISCOUS DAMPING SOIL LAYER CONSIDERING THREE-DIMENSIONAL WAVE EFFECT AND ITS APPLICATIONS

从三维轴对称土体模型出发,考虑土体三维波动效应,对黏弹性支承桩在任意竖向激振力作用下与土体的耦合作用特性进行了研究。假定桩为竖直、弹性、等截面体,土为线性黏弹性体,其材料阻尼为黏性阻尼。利用拉普拉斯变换,将定解问题转换到拉普拉斯域内求解。通过引入势函数,将土体位移进行分解,从而将土体动力平衡方程进行解耦,求解得到土体的振动模态形式,再利用该解,以小应变条件下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,得到拉普拉斯域内桩的位移函数解析解,进而可得到桩顶速度导纳函数解析解,采用卷积定理和傅里叶逆变换,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。基于所得解对速度导纳曲线和速度反射波曲线进行了量纲一的参数讨论,以揭示桩的纵向振动特性,为基桩动测提供理论和实践上的指导。

Modeling soil as a 3D axisymmetric continuum and taking its 3D wave effect into account,the interaction between soil layer and pile with viscoelastic bottom boundary undergoing arbitrary vertical load is theoretically investigated.The investigation will be of significance for dynamic test of pile.The pile is assumed to be vertical,elastic and of uniform cross-section,and the soil is considered as a linear viscoelastic layer with viscous damping.With Laplace transforms,the question can be solved in Laplace domain.With the aid of two potentials,the displacement of soil is decomposed and the dynamic equilibrium equation of soil layer is uncoupled and solved first.Thus the vibration modes of the soil layer are obtained to analyze the pile response.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 displacement function in Laplace domain is yielded,so are the corresponding analytical solutions for the mobility at the level of the pile head in frequency domain.With 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 derived.Based on the solutions proposed herein,a parametric study of the effect of some governing dimensionless parameters on mobility curves and velocity reflection wave curves is conducted to illustrate the main features of longitudinal vibration of pile.