A simplified three-parameter model for analyzing torsional vibration of rectangular foundations on layered soil

Dynamic soil-structure interaction (SSI) significantly impacts structural vibration. Over the past few decades, numerous simplified models were developed to analyze dynamic SSI on homogeneous soil. In this study, however, a lumped-parameter model is adopted to investigate the dynamic behavior of rectangular foundations overlying nonuniform soil. The simplified three-parameter model is utilized to analyze the torsional vibration of rectangular foundations on layered soil with linearly varying shear-wave velocities. Non-dimensional parameters (shear-wave velocity ratios, layer depth ratios, and mass ratios) are also investigated herein. The frequency-magnification curves of the foundation using three-parameter model are found to agree well with theoretical solutions. Consistent agreements are also observed at the resonant response and its corresponding frequency ratio. Additionally, the resultant resonant magnification factors against mass ratios clearly show the impacts of the whipping effect resulting from soil-foundation interactions. The proposed model excels in simulating layered soil and includes fewer parameters than existing lumped-parameter models. The proposed model also demonstrates the adaptivity and reliability to simulate the dynamic responses calculated from the published in-situ experimental data. The time-domain application based on the proposed model effectively estimates the structural displacement of the soil-foundation-superstructure system. This research could contribute to the SSI analysis regarding the torsional vibration of a foundation on nonuniform soil.