Wave Diffraction by Rigid Foundations

In the design of a building to resist ground shock, evaluation of the dynamic response of the structure is necessary due to the stress waves that impinge on the foundation. Unfortunately, specifying the incoming waves is usually not possible because of their complexity. Instead, structural engineers have available only displacement, velocity, and acceleration time histories as measured at some location during actual tests or events. Consequently, unique definition is not possible of a wave field which produced these given free-field motions. Engineering practice has been to avoid this difficulty by assuming that the structure foundation will move with the specified free-field motion if its inertia is neglected. Then, the foundation inertia forces due to the free-field accelerations are included in the building equations of motion as forcing functions. Lysmer and Waas have observed that this assumption has no basis in rational mechanics. Thus, in order to suggest a heuristic basis, examples of wave diffraction by rigid inclusions in elastic media with known exact solutions are presented in this note, to show that the usual assumptions can be expected to give conservative estimates of response. A mechanical analog for the structure-medium interaction problem can be obtained if the interaction impedance is linearized. Effects of this linearization are also shown herein.