Numerical Block-Based Simulation of Rocking Structures Using a Novel Universal Viscous Damping Model

Abstract

Unreinforced masonry structures, particularly façade walls, are seismically vulnerable due to their weak connections with adjacent walls, floors, and/or roofs. During an earthquake, such walls formulate local mechanisms prone to out-of-plane collapse. This behavior has been largely investigated using classical rocking theory, which assumes the structure responds as a rigid body undergoing rocking motion, with energy dissipation at impact. Due to the complexity of the problem, however, e.g., number of degrees of freedom or boundary conditions, numerical block-based modeling is gaining momentum. However, numerical models lack a consistent and reliable treatment of the energy loss at impact. This paper bridges the gap between the well-established energy loss of classical rocking theory and the treatment of damping in numerical modeling. Specifically, it proposes an equivalent viscous damping model through novel ready-to-use predictive equations that capture the dissipative phenomena during both one-sided and two-sided planar rocking motion. The results reveal a satisfactory performance of the proposed model through comparisons with experimental results from literature and highlight its universality and robustness through applications of the model in fundamentally different block-based numerical modeling software.

Seismic rocking simulation of unreinforced masonry parapets and façades using the discrete element method

“…Damping was treated as a dashpot applied at the nodes on the interfaces, reducing the velocity of the block, and a procedure similar to that proposed herein was adopted to correlate e and ζ n . Vlachakis et al 57 . found that the geometrical relationship h / b greatly influenced the relationship between e and ζ n , similar to the findings of the study reported here.…”

“…Recently Vlachakis et al 57 . published a study expanding the research performed by Tomassetti et al 56 .…”

“…the relationship developed to correlate e and ζ n was applied to two numerical models: a rocking block discretised into an FEM deformable mesh for inclusion in the software Abaqus CAE, and to a rocking block discretized into an assembly of elements simulating the individual bricks when using 3DEC. However, the model presented herein used a single block with elastic deformations lumped at the base interface, which constitutes a considerable difference with respect to the study undertaken by Vlachakis et al 57 . Additionally, for the two‐sided rocking problem Vlachakis et al 57 .…”

“…by obtaining a correlation between e and ζ n to be implemented in numerical models. Similarly, to the model reported herein, Vlachakis et al 57 . included correlations to use viscous damping strategies to be applied on both two‐sided and one‐sided rocking problems.…”

“…found that the geometrical relationship h / b greatly influenced the relationship between e and ζ n , similar to the findings of the study reported here. In the study performed by Vlachakis et al 57 . the relationship developed to correlate e and ζ n was applied to two numerical models: a rocking block discretised into an FEM deformable mesh for inclusion in the software Abaqus CAE, and to a rocking block discretized into an assembly of elements simulating the individual bricks when using 3DEC.…”