A simple solution technique for evaluating the response of a surface or embedded foundation under vertical vibrations in a homogeneous soil has been developed. The effects of soil nonlinearity on shear modulus and material damping, frequency on stiffness and radiation damping, and embedment of foundation on stiffness and radiation damping have been considered. A computer program has been developed based on the Elastic Half Space (EHS) analog technique (Lysmer and Richart, 1966), to compute the response amplitude of both surface and embedded footings. The computed response has been verified by comparing it with measured data from Novak (1970). The predicted response is underestimated in all cases because the (EHS) analog computed radiation damping is overestimated. A modification factor, λ, has been proposed and applied to correct the estimated radiation damping. A unique relationship between λ, (correction factor for radiation damping), and shear strain (γ) has been established for field use. A rational correction factor to radiation damping for computing vibration footing response has been proposed for the first time and this has been shown to provide computed results which compare quite well to measured results
