Implementation and stability analysis of discrete-time filters for approximating frequency-dependent impedance functions in the time domain

This work presents the implementation and stability analysis of a method to account for inertial soil-structure interaction (SSI) in time-history analyses, which is achieved by approximating nominally frequency-dependent foundation impedance functions in the time domain using discrete-time digital filters. The method is demonstrated using a multi-story shear building supported by a rigid disk foundation resting atop a uniform soil half-space and subjected to a horizontal ground motion. The soil-foundation-structure system's equations of motion are numerically integrated to determine its time-history response. The results are verified through comparison to those obtained both through frequency domain analyses and through sampling of the foundation impedance functions at a representative frequency. Numerical stability of the method is examined both analytically and numerically; and it was determined that the stability of the filter and the stability of the time stepping method adopted do not guarantee that their combination will be stable as well.