On the Reduction of Radiation Damping of Dynamic Foundation on Gibson Elastic Halfspace

For dynamic machine foundations, it is widely acknowledged that the radiation damping ratio estimated by Lysmer’s analogy method is often overestimated, leading to the adoption of modifications in design codes across various nations. This study explores the underlying reasons for this overestimation, focusing on the less recognized impact of subsoil modulus variation with depth, particularly in Gibson soil. Gibson soil, characterized by a depth‐dependent modulus, can significantly reduce radiation damping even in homogeneous conditions. The research employs a cone model to analyze the vertical vibration of a circular disk foundation on Gibson soil, yielding an analytical solution for the impedance function. This study establishes an analytical relationship between Gibson soil and radiation damping reduction for the first time, revealing the independent mechanism of how the modulus varies with depth. An extended cone model is proposed to overcome the complexity of the traditional Hankel transform method. This model achieves a frequency‐independent closed‐form solution for Gibson soil foundation impedance. Results verify that Gibson soil has a lower damping ratio than uniform soil layers, with an average reduction factor of 0.65–0.85. These findings provide a theoretical basis for revising seismic codes (GB 50699‐2011) and propose a new damping calculation formula that considers the modulus gradient.