Seismic Response of Hemispherical Foundation

A time domain finite element method has been used to investigate the response to seismic waves of rigid, three-dimensional, embedded foundations. The method eliminates the influence of artificial grid boundaries by completing the transient solution prior to the arrival of any nonphysical reflections. The accuracy of the numerical procedure has been examined by comparison with analytic solutions; discrepancy is less than 5% at all frequencies up to β/a in which β=the shear wave speed of the embedment medium; and a is the foundation radius. For a hemispherical foundation, the scattering of vertically incident S waves reduces the higher frequency horizontal translation of the foundation compared with the free-field motion but introduces a significant rocking component that is absent from the free field.