Coupled Horizontal and Rocking Vibration of Embedded Footings

Abstract

The prediction of the coupled response to horizontal forces is of major importance for the design of footings exposed to dynamic effects. The theory of surface footings greatly overestimates the real response and neglects the fact that the footings are founded beneath the surface of the ground, i.e. partly embedded. This latter factor considerably affects the footing vibrations in that it reduces the resonant amplitudes and increases the resonant frequencies.An approximate analytical solution was developed in this paper and the theoretical response curves were compared with field experiments. Closed form formulas were obtained that are simple enough to be directly used in design. The approximate analytical solution is better able to predict the coupled response of embedded footings than that of surface footings. The response is usually dominated by the first resonant peak with the second resonant peak entirely suppressed. The derived formulas for equivalent stiffnesses and damping coefficients due to soil can be introduced into the solution of any structure.