Considering the interactions between the embedded foundation and the soil

the torsional vibrations of a rigid cylindrical foundation partially embedded in transversely isotropic saturated soil are analysed. Assuming both the side face and bottom surface of the foundation are perfectly bonded to the soil

the reaction torques that the side soil and bottom soil acted on the foundation are gotten from basic dynamic equations of the poroelastic medium. According to the dynamic equilibrium equations of a foundation subjected to harmonic torque

the torsional vibrations of an embedded cylindrical foundation are presented. Subsequently

the angular amplitude of the foundation

the equivalent stiffness and damping coefficients of the soil are expressed explicitly. Selected examples are presented to investigate the influence of relevant parameters on the results.