Dynamic impedances of ring disks buried in arbitrary depths

This paper addresses the vertical, horizontal and rocking vibrations of a rigid ring disk, with especially small radial wall-thicknesses, embedded in any depth of a fully saturated poroelastic half-space. The mixed boundary value problem is expressed in terms of dual integral equations that are solved semi-analytically with all boundary conditions satisfied. Numerical results of quasi-static stiffness, dynamic impedances (including dynamic stiffness and radiation damping ratio) are obtained. The influence of Poisson's ratio, soil permeability, disk embedded depth and excitation frequency on the stiffness and damping ratio of the ring disk is illustrated. It is found that for a ring disk, although its thickness-to-radius ratio is only about 2%-4%, its vertical, horizontal and rocking impedances are around 70% of the corresponding values of a circular disk. Besides, the vertical, horizontal and rocking stiffness of a deeply embedded ring disk is all about 2.0 times that of the surface ring disk. Simplified equations for the initial base stiffness of pipe piles/caissons are obtained. The results can be combined with Winkler-based models to address thin-walled pile/caisson-soil interaction problems in the field of offshore wind turbines or bridges.