Formulas and charts for impedances of surface and embedded foundations

TLDR: In this paper, a complete set of algebraic formulas and dimensionless charts are presented for readily computing the dynamic stiffnesses and damping coefficients of foundations harmonically oscillating on/in a homogeneous half-space.

Abstract: A complete set of algebraic formulas and dimensionless charts is presented for readily computing the dynamic stiffnesses (\IK\N) and damping coefficients (\IC\N) of foundations harmonically oscillating on/in a homogeneous half-space. All possible modes of vibration, a realistic range of Poisson’s ratios, and a practically sufficient range of oscillation frequencies are considered. The foundations have a rigid basemat of any realistic solid geometric shape. The embedded foundations are prismatic, having a sidewall-soil contact surface of height \Id\N, which may be only a fraction of the embedment depth \ID\N. Two numerical examples illustrate the use of the formulas and charts and elucidate the role of foundation shape and degree of embedment on radiation damping for various modes of vibration. A companion paper (Gazetas and Stokoe 1991) presents supporting experimental evidence from model tests. The two papers aim at encouraging the practicing engineer to make use of results obtained with state-of-the-art formulations, when studying the dynamic response of foundations.