Enhanced identification method for rational approximation models of unbounded soil to ensure stability in soil-structure interaction systems

Artificial boundary condition methods provide a simple and efficient approach for simulating wave propagation and dynamic behavior in unbounded soil for soil-structure interaction (SSI) analyses. While commonly used spring–dashpot boundaries are easy to implement, their neglect of frequency-dependent dynamics at the soil's truncated boundaries often limits accuracy. Dynamic impedance functions offer a more precise representation of these frequency-dependent effects. However, stable identification of rational approximation models for dynamic impedance remains a significant challenge in SSI systems. Recent studies reveal that even stable rational approximations of the soil alone may cause instability once coupled with the superstructure—an issue yet to be resolved. This study first presents a stability analysis method for SSI systems based on gain margin, uncovering that the instability of the coupled system arises from rational approximation model identification errors, which induce low-frequency negative damping. To counter this issue, we proposed an enhanced identification method, which introduces a frequency-domain optimization framework with positive phase constraints, effectively mitigating the negative damping and suppressing phase distortion while preserving model accuracy. The proposed method is validated through numerical simulations and time-domain analysis, demonstrating its ability to maintain the stability of SSI systems without compromising their physical fidelity. The proposed phase-constraint identification method addresses a critical gap in the stable modeling of semi-infinite soil systems and enhances the reliability of SSI simulations in earthquake engineering.