下卧基岩饱和地基中埋置刚性基础的竖向振动问题研究

Vertical vibration of rigid embedded foundations in saturated soil overlying bedrock

基于Biot提出的饱和土波动方程,研究了埋置于单层饱和地基中的有质量的刚性圆柱基础的竖向振动问题。运用Hankel积分变换求解饱和土基本动力方程,并考虑基础与地基接触面的混合边值条件,求得了基础底面和基础侧面的动反力,结合基础振动的动力平衡方程,得到了基础竖向振动振幅和地基等效动力刚度的表达式。数值分析结果表明:下卧基岩饱和地基的等效动力刚度和基础振动振幅都呈现出明显的波动现象,土层厚度、基础埋深比、基础质量比对埋置基础的竖向振动有很大影响。

Based on the Biot＇s theory of poroelastodynamics, the vertical vibrations of a massive, rigid cylindrical foundation embedded in single-layered saturated soil were studied. At first the goveming differential equations of saturated soil were solved by Hankel integral transform. Then, considering the mixed boundary value conditions at the interface between the foundation and the soil, the dynamic reaction at the base of foundation and along the side of foundation were obtained. Subsequently, the vertical displacement amplitude of the foundation and the equivalent dynamic impedance of the saturated soil overlying bedrock were derived by combining the dynamic equilibrium equation of the foundation. Selected numerical results indicate that the displacement amplitude and the dynamic impedance show obvious fluctuations, and that the soil layer thickness, the depth ratio of the foundation, the mass ratio of the foundation and the soil permeability have significant influence on the vertical vibrations of embedded foundations.