Development of New Stiffness and Damping Expressions for Footing Vibrations

New expressions for stiffness and radiation damping, which have been developed for a new forcing function, are based on the simple equation of wave propagation in a perfectly elastic half space for different modes of vibrations, particularly vertical and horizontal vibrations. A differential equation including the effect of foundation mass is presented and the results of the amplitudes of vibration obtained from this differential equation are compared with those in the standard differential equation in soil dynamics textbooks. Furthermore, added soil masses for vertical and horizontal vibrations are also derived based on the equation of wave propagation and discussed with other findings. Finally, this paper also compared different ways of using the total damping, which is composed of radiation damping and internal damping