A Simplified Mechanical Model for Rocking Structures on Compliant Foundations

Housner’s classical rocking model assumes a rigid base, often leading to inaccurate seismic assessments in real-world soil conditions. This study quantitatively establishes the applicability limits of the rigid-base assumption and defines a reference range for its validity. To bridge this gap, a novel Soil-Structure Interaction (SSI)-rocking model is formulated via the Lagrange Equation, capturing the coupled dynamics between rocking blocks and compliant foundations. Crucially, a closed-form relationship is derived to correlate the analytical model’s interface stiffness with the shear and Young’s moduli used in industrial finite element (FE) software. Our findings reveal that rocking behavior depends not only on soil stiffness but also on the inherent stiffness of the structure. Consequently, a relative stiffness parameter is introduced to bridge the analytical and numerical frameworks. Validation using LS-DYNA confirms the model’s precision across varying base stiffnesses. Results indicate that softer soils significantly alter rocking initiation thresholds and amplify peak angles. This proposed analytical model provides a computationally efficient, FE-compatible tool to improve stability predictions and design strategies for unanchored structures in earthquake-prone regions.