Response of circular flexible foundations subjected to horizontal and rocking motions

A methodology using modal analysis is developed to evaluate dynamic vertical displacements of a circular flexible foundation resting on soil media subjected to horizontal and rocking motions. The influence of the soil reaction forces on the foundation is considered by introducing modal impedance functions, which can be determined by an efficient procedure with ring elements. The displacements of the foundation can then be easily solved by modal superposition. Parametric studies for modal responses of the flexible foundation indicate that the coupled response of the foundation is significantly influenced by relative stiffness among the foundation and the soil medium, vibration frequency range, foundation mass, and boundary contact conditions. The welded boundary condition should be considered to predict the coupling response while the relaxed boundary condition may be used to predict approximately the vertical displacements. As a foundation with a relative stiffness ratio more than three, it is found that the foundation can be considered as rigid to calculate coupling displacements. For a slightly flexible foundation, considerations of three modes are sufficient enough to obtain accurate foundation responses. Moreover, at low frequencies, the coupling effect due to higher mode can be neglected.