Vertical vibration of rigid embedded foundations in saturated soil overlying bedrock

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 governing 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.