The rocking response of rigid bodies has been extensively studied in Mechanics and Civil Engineering, especially following the foundational work of Housner. While prior research has primarily examined symmetric blocks, structures that react the same way to excitations in either direction, many practical configurations involve asymmetry, where the centers of mass and geometry do not coincide. This asymmetry results in direction-dependent responses under dynamic loading. This study explores the seismic behavior of asymmetric rigid blocks supported by a dual isolation system, featuring both horizontal and vertical components, with particular emphasis on characterizing and understanding their nonlinear dynamic response. The governing equations of motion are derived, accounting for both rocking and full-contact phases, as well as uplift and impact conditions. The horizontal isolation is modeled using a Bouc-Wen hysteretic formulation, while the vertical isolation system is represented with a Kelvin-Voigt viscoelastic model. The first part concerns the seismic analysis of the system. As base excitation, three earthquake horizontal and vertical records are selected accounting for their spectral content and PGA. The results are arranged in rocking maps and comparisons among the systems referring to symmetric rigid blocks and those referring to asymmetric blocks with increasing eccentricity are performed to examine the role of the asymmetry of blocks protected with the dual base isolation. Results show that vertical isolation, when combined with horizontal isolation, enhances the block’s ability to remain in full-contact compared to the case with horizontal isolation alone. The second part focuses on the overturning mechanisms exhibited by asymmetric rigid blocks equipped with the previously discussed dual base isolation system. To this end, the system is subjected to horizontal and vertical impulsive one-sine base accelerations, and the resulting overturning spectral maps are constructed. The analysis uncovers previously unidentified overturning modes specific to dual-isolated asymmetric blocks.
Amoroso et al. (Sat,) studied this question.