Approximate soil-structure interaction analysis by a perturbation approach: The case of stiff soils

• New expressions for approximate multi-modal analysis of building-foundation systems.
• Analysis and interpretation of perturbed structural and foundation modes.
• Validation of the proposed approach through numerical analysis of a 9-story structure.
• Assessment of the range of validity of classical normal mode-based approaches.

An approximate solution of the classical eigenvalue problem governing the vibrations of a structure on an elastic soil is derived through the application of a perturbation analysis. For stiff soils, the full solution is obtained as the sum of the solution for a rigid-soil and small perturbing terms related to the inverse of the soil shear modulus. The procedure leads to approximate analytical expressions for the system frequencies, modal damping ratios and participation factors for all system modes that generalize those presented by other authors for the fundamental mode. The resulting approximate expressions for the system modal properties are validated by comparison with the corresponding quantities obtained by numerical solution of the eigenvalue problem for a nine-story building. The accuracy of the proposed approach and of the classical normal mode approach is assessed through comparison with the exact frequency response of the test structure.