An equivalent viscous damping proposal for block-based rocking models

Masonry structures have been observed to display a high vulnerability to failure under seismic action. This stems from the fact that their structural configurations usually lack adequate connections among the distinct elements, resulting in the formation of local mechanisms experiencing Out-Of-Plane (OOP) collapse. In this context, rocking dynamics has proven to be a valuable methodology for the analysis of masonry walls. Classical rocking theory can provide a fast solution to the dynamic phenomena taking place if simple configurations are examined. Nevertheless, as the degrees of freedom and the boundary conditions increase, the complexity increases, and thus the classical rocking theory becomes impractical. In the meantime, recent developments in computational modelling of masonry structures are gaining significant attraction. This includes block-based models which inherently consider the complexity of the problem and enable the solution to be obtained easily in the discretised spatial and time domains. However, despite their widespread use, applications of such models usually lack a reliable treatment of damping. The present work attempts to bridge the gap between the well-established energy loss of the classical rocking theory and the treatment of damping of block-based computational models. To do so, the dynamics of the problem are reviewed and an equivalent viscous damping model is proposed. A unilateral dashpot formulation allows the replication of the impulsive nature of the energy loss at impact. Afterwards, a calibration methodology is adopted for the practical range of the problem's parameters and a ready-to-use equation is provided, which respects energy equivalence. The performance of the proposed damping model is also evaluated through comparisons with experimental results.