Radiation damping for rigid foundations. Approximate expressions

The dynamic response of machine foundations was one of the first problems studied in soil dynamics with results going back to the 1930s. A number of approximations and graphical results were proposed in the 60s. In this paper we present a series of approximate expressions for the natural frequencies and effective damping of rigid masses on the surface of an elastic half space subjected to both vertical and coupled horizontal-rocking harmonic excitations. The formulas are obtained using the approximate expressions for the dynamic stiffness of circular foundations suggested by Veletsos et al [1, 2] for two different values of Poisson’s ratio of the soil. For the vertical case the expressions are only a function of the mass ratio (ratio of the mass of the foundation to an effective mass of soil) and of Poisson’s ratio. For the horizontal-rocking case they depend also on the ratio of the height of the foundation to its equivalent radius (a slenderness ratio)