A Simplified Mechanical Model for Rocking Structures on Compliant Foundations

Housner’s classical rocking model assumes a rigid base, which often leads to inaccurate seismic assessments under 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 address these limitations, a novel soil–structure interaction (SSI) rocking model was developed using Lagrange’s formulation, incorporating an event–driven spring–dashpot mechanism to characterize contact forces. Validation against LS–DYNA simulations and existing compliant base models confirms high predictive accuracy across diverse geometries and ground motions. Crucially, an empirical formulation for the interface stiffness of rocking structures was derived to ensure the alignment of the proposed analytical model with numerical observations, thereby enhancing its practical utility in industrial design. Our findings reveal that rocking behavior depends not only on soil stiffness but also on the inherent stiffness of the structure. Specifically, soft soils significantly alter rocking initiation thresholds and amplify peak angles. The proposed SSI–rocking model provides a computationally efficient and FE–compatible tool for optimizing the seismic stability of unanchored structures on flexible foundations.