A blind prediction contest was organized to evaluate the ability of different modeling approaches to simulate the seismic rocking response of a full‐scale four‐column podium structure. The structure was tested on a shake table, and was subjected to two bidirectional ground motion ensembles comprising 100 synthetic records each. This short communication presents the main assumptions and results from the model, developed using the distinct element method, which provided the second‐best prediction of the experimental results. A comparison of the model predictions and the experimental results demonstrates that the numerical model was generally able to reproduce the large displacements induced by the more intense ground motion ensemble, while tending to overestimate the displacements of the less intense earthquake ensemble. This overestimation of the response was reduced through the inclusion of damping in the system. However, the addition of damping greatly increased the solve time, which is problematic for a competition, and in the case of the more intense ground motion ensemble also resulted in an underprediction of the maximum response of the structure.

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This paper presents a user-friendly, CAD-interfaced methodology for the rapid seismic assessment of historic masonry structures. The proposed multi-level procedure consists of a two-step analysis that combines upper bound limit analysis with non-linear dynamic (rocking) analysis to solve for seismic collapse in a computationally-efficient manner. In the first step, the failure mechanisms are defined by means of parameterization of the failure surfaces. Hence, the upper bound limit theorem of the limit analysis, coupled with a heuristic solver, is subsequently adopted to search for the load multiplier’s minimum value and the macro-block geometry. In the second step, the kinematic constants defining the rocking equation of motion are automatically computed for the refined macro-block model, which can be solved for representative time-histories. The proposed methodology has been entirely integrated in the user-friendly visual programming environment offered by Rhinoceros3D + Grasshopper, allowing it to be used by students, researchers and practicing structural engineers. Unlike time-consuming advanced methods of analysis, the proposed method allows users to perform a seismic assessment of masonry buildings in a rapid and computationally-efficient manner. Such an approach is particularly useful for territorial scale vulnerability analysis (e.g., for risk assessment and mitigation historic city centres) or as post-seismic event response (when the safety and stability of a large number of buildings need to be assessed with limited resources). The capabilities of the tool are demonstrated by comparing its predictions with those arising from the literature as well as from code-based assessment methods for three case studies.

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.

Summary Failure of masonry structures generally occurs via specific collapse mechanisms which have been well documented. Using rocking dynamics, equations of motion have been derived for a number of different failure mechanisms ranging from the simple overturning of a single block to more complicated mechanisms. However, most of the equations of motion derived thus far assume that the structures can be modelled as rigid bodies rocking on rigid interfaces with an infinite compressive strength—which is not always the case. In fact, crushing of masonry—commonly observed in larger scale constructions and vertically restrained walls—can lead to a reduction in the dynamic capacity of these structures. This paper rederives the rocking equation of motion to account for the influence of flexible interfaces, characterized by a specific interface stiffness as well as finite compressive strength. The interface now includes a continually shifting rotation point, the location of which depends not only on the material properties of the interface but also on its geometry. Expressions have thus also been derived for interfaces of different geometries, and parametric studies conducted to gauge their influence on dynamic response. The new interface formulations are also implemented within a new analytical modelling tool that provides a novel approach to the dynamic analysis of masonry collapse mechanisms. Finally, this tool is exemplified, along with the importance of the interface formulation, by evaluating the collapse of the Dharahara Tower in Kathmandu, which was almost completely destroyed during the 2015 Gorkha earthquake.