The influence of a deformable foundation on the response of buildings to earthquake motion is examined. The study is divided into two parts; the vibration of the base of the building on the foundation medium, and the response of the whole building-foundation system.
Studied first are the forced horizontal, rocking and vertical harmonic oscillations of a rigid dis c bonded to an elastic half-space, which is considered as a mathematical model for the soil. The problem,formulated in terms of dual integral equations, is reduced to a system of Fredholm integral equations of the second kind. For the limiting static case these equations yield a closed form solution in agreementwith that obtained by others.
Using the force-deflection relations for the base, the equations of motion of linear building-foundation systems are solved by both direct and transformmethods.It is shown that, under assumptions which appear to be physically reasonable, the earthquake response of the interactionsystem reduces to the linear superposition of the responses of damped, linear one-degree-of-freedom oscillators subjected to modified excitations. This result is valid even for systems that do not possessclassical normal modes. Explicit approximations in terms of the parameters of the system are obtained for the dynamic properties ofthe one-degree-of-freedom oscillator which is equivalent to a single story building-foundation system. For multi-story buildings it is shown that the effect of an elastic foundation, as measured by the change inthe natural frequencies of the building, is negligible for modes higher than the first for many types of building structures.
