| This study focuses on the approximate analysis of soil-structure interaction problems, specifically on the application of classical modal analysis for coupled horizontal-rocking vibrations of plane structures resting on a linear elastic soil. Although the classical modal approach provides a non-rigorous solution, it is particularly meaningful as it offers physical insight into the nature of soil-structure interaction effects.;After validating the numerical algorithm by comparison with earlier works, a comprehensive assessment of the classical modal approach is performed, based on the analysis of a nine-story building. The accuracy of the approximate solution is quantified by introducing two measures of error of the steady-state response. The source of the lack of accuracy of the approach is investigated by analyzing the off-diagonal terms of the modal damping matrix. The effects of interaction on the dynamic properties of the structure are clearly shown through a parametric study of the test structure, and they are interpreted by comparison with different limit cases.;A better general understanding of the soil-structure interaction is provided by introducing an equivalent model, consisting of a single degree of freedom oscillator on an elastic soil. The equivalent model is used to approximate each system mode, once the modal properties of the structure on a fixed-base are known.;New approximate analytical expressions for the system frequencies, modal damping ratios and participation factors for all modes are derived through the application of a perturbation analysis. The proposed expressions could be effective in performing preliminary analysis, validating other results, and being incorporated into codes or guidelines. |
