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.
Highlights
Masonry structures display high vulnerability to seismic action— threatening human lives, built assets, and a major part of our cultural heritage (Bruneau 1994; Penna et al 2014)
This paper presented a novel viscous damping model that derives equivalence between the damping of numerical block-based models and the impulsive nature of energy loss of the classical rocking theory
New predictive equations are proposed and calibrated through over 1,000 free-rocking numerical simulations, which correlate the damping ratio of the numerical model to the coefficient of restitution of the statistically accurate classical rocking theory, for both the two-sided and one-sided rocking cases. The former is representative of the behavior of structures such as parapet walls, which are free to rock in both positive and negative directions, with impact only against the base, whereas the latter is more commonly observed in the case of façades, which are generally free to rock in only one direction, with impact taking place against the base and transverse walls
Summary
Masonry structures display high vulnerability to seismic action— threatening human lives, built assets, and a major part of our cultural heritage (Bruneau 1994; Penna et al 2014). Tomassetti et al (2019) followed a calibration process of a single degree of freedom (SDOF) analytical formulation of rocking structures adopting different formulations of viscous models (i.e., CDC, CDR, and SDR), and the influences on the response of additional parameters, such as the interface stiffness, rocking amplitude, and aspect ratio, were investigated. By adjusting the damping ratio of the viscous damping model, energy equivalence between the two modeling approaches can be achieved To this end, a calibration methodology is presented, with the aim of providing generalized predictive ξ–e relationships applicable to a variety of block-based (numerically simulated) structures that undergo either one-sided or two-sided rocking motion. The proposed numerical (viscous damping) model shows adequate adaptability and robustness to such case-specific experimental characteristics
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