Vertical dynamic impedance of the support plate of the Rod-less drilling rig in layered soil

The vertical dynamic response of the support plate of the Rod-less drilling rig in layered soil is theoretically investigated. The soil layers are modeled as a set of viscoelastic continuous media, and the distributed Voigt model is proposed to simulate the dynamic interactions of the adjacent soil layers. Meanwhile, the support plate is regarded as an annular friction pile with a certain radian and can be divided into several plate segments allowing for soil layers. The governing equation of soil vibration is solved by virtue of the Laplace transform and the separation of variables method. Then the vertical dynamic impedance at the bottom of the support plate is derived by means of the impedance function transfer method as well as the force and displacement continuity conditions at the soil-plate interface. By means of the inverse Fourier transform and convolution theorem, the velocity response in the time domain can also be obtained. The reasonableness of the assumptions of the support plate and soil-layer interactions has been verified by comparing the present solutions with dynamic experiments on a full-scale plate in the field. It is shown that the solution derived in this study agrees better with the experimental one than the more limited solution of Novak. An extensive parametric study has been conducted to investigate the effects of major parameters.