Two-dimensional approximations to the three-dimensional soil-structure interaction problem

The feasibility of representing a three-dimensional soil-structure interaction problem by a plane strain model, and the errors involved in such representation, were studied. By comparing the rocking and translational force-displacement relationships for a rigid circular foundation placed on an elastic half-space and the corresponding relationships for a strip footing placed on an elastic half-plane it was found that it is not possible to obtain a two-dimensional representation that will approximate both the dynamic stiffness and radiation damping over a reasonable range of frequencies. Several two-dimensional models were considered and a measure of the errors involved is presented. In general, the two-dimensional models overestimate the radiation damping associated with the three-dimensional problem. To study the effects that the use of a two-dimensional plane strain model may introduce in the solution of the soil-structure interaction problem for typical nuclear power plants, a comparison was made between the system frequencies and modal dampings obtained for three and two-dimensional models. The corresponding response at the top of the containment shell, top of the internal structure, and base slab for a particular earthquake were also compared. It was found that by properly selecting the two-dimensional model it was possible to obtain close approximations to the system frequencies. However, since the dampings associated with the low frequency modes are overestimated, the earthquake response of the structure, as obtained by the two-dimensional model, is underestimated to a significant degree.