Effect of Flexibility on Impedance Functions for Circular Foundation

This paper investigates the effect of foundation rigidity on impedance functions for a circular foundation on a viscoelastic soil medium. In addition to vertical and rocking impedances, the paper also investigates the influence on coupling impedance for horizontal and rocking motions of foundation and horizontal impedance. To generate impedance functions for flexible foundation, a substructure technique is used. For the substructure of the flexible foundation, classical plate theory with neglecting inertial force is employed to obtain the deformation of the foundation due to the interaction stress. For the substructure of the soil medium, the technique, which can deal with wave equations in cylindrical coordinates with arbitrarily prescribed boundary conditions, is employed to obtain the displacement field in the soil medium due to the interaction stresses. Then, with the help of the variational principle, the displacement continuity condition of both substructures is imposed to generate the impedances for the flexible foundation. To demonstrate the effectiveness of the presented procedure, comparison with some previous numerical results is made. Selected numerical results of the presented procedure are presented. Also, comparison between results with and without the assumption of relaxed stress condition is given in order to show the significance of the assumption.