The out-of-plane (OOP) dynamic behavior of unreinforced masonry (URM) gable walls was investigated in this paper using a high-fidelity block-based numerical modeling approach, building on the participation of the authors in the ERIES SUPREME blind prediction competition. In this paper, the numerical models developed for the competition were updated based on the experimental data published after the competition to further improve accuracy. The improvement was obtained by slight recalibration of mortar joint tensile strength and friction between the walls and the loading set-up. The updated models were also adopted to simulate a third wall originally excluded from the competition. The models were then used to complement the experimental campaign with additional configurations in a parametric study. Specifically, the influence of roof-wall connections and pre-existing damage on the performance of the gable walls were examined to address gaps identified in both experimental and numerical studies of the past. Stronger roof-wall connections, while improving global stability and increasing wall OOP strength in the static regime by up to 140%, led to collapse at dynamic loading intensities reduced by an average of 28% and up to a maximum of 57%. This early collapse resulted from the transfer of larger dynamic demands to the gable walls. This higher demand transfer also caused earlier damage initiation and considerable changes in collapse mechanisms, effects not captured by static analysis, highlighting the uncertainties governing dynamic behavior and the need for robust methodologies to address them. Finally, light pre-damage, modelled in this study as a crack at the base of the walls, had only a minor influence on failure mechanisms and OOP resistance.

This paper deals with the blind prediction of the dynamic out-of-plane (OOP) response of unreinforced masonry gables via block-based modelling within a competition organized by ERIES SUPREME. Three gable wall specimens were tested at the EUCENTRE foundation in Pavia, Italy, under incremental shaking-table earthquake loading until collapse. In the tests, each wall was subjected to distinct boundary conditions, simulating interactions with stiff, flexible, and semi-flexible diaphragms. The competition challenged participants to predict the responses of two of these walls, replicating stiff and flexible diaphragms, with minimal access to experimental data and outcomes, emphasizing the need for reliable modeling techniques. The authors utilize a novel 3D block-based model, originally developed for cyclic quasi-static responses and recently extended to dynamic one- and two-way OOP bending. Both the walls and the loading set-up are simulated. The masonry assembly of the walls is conceived as solid expanded blocks connected via zero-thickness planar joints in the former. The robustness of the predictions is enhanced through a sensitivity analysis exploring the influence of variations in mechanical properties, vertical and dynamic loading assumptions, and damping on the response. Numerical models predict the key experimental observations, such as the collapse onset, failure mechanisms, displacement demands, and dynamic responses, with good accuracy, achieving the best blind prediction results. Indeed, the modeling approach shows great capability to capture complex dynamic interactions, highlighting its potential in complementing physical testing. Moreover, the simulation is able to successfully predict not only the global response of the gables, but also to reproduce several details affected by the test set-up and loading assumptions. The modeling strategy appears a good candidate for sensitivity and probabilistic analysis, capable of extending the current understanding of seismic performance in masonry structures and overcoming limitations inherent in experimental methods.

Masonry structures, although classically suitable to withstand gravitational loads, are sensibly vulnerable if subjected to extraordinary actions such as earthquakes, exhibiting cracks even for events of moderate intensity compared to other structural typologies like as reinforced concrete or steel buildings. In the last half-century, the scientific community devoted a consistent effort to the computational analysis of masonry structures in order to develop tools for the prediction (and the assessment) of their structural behavior. Given the complexity of the mechanics of masonry, different approaches and scales of representation of the mechanical behavior of masonry, as well as different strategies of analysis, have been proposed. In this paper, a comprehensive review of the existing modeling strategies for masonry structures, as well as a novel classification of these strategies are presented. Although a fully coherent collocation of all the modeling approaches is substantially impossible due to the peculiar features of each solution proposed, this classification attempts to make some order on the wide scientific production on this field. The modeling strategies are herein classified into four main categories: block-based models, continuum models, geometry-based models, and macroelement models. Each category is comprehensively reviewed. The future challenges of computational analysis of masonry structures are also discussed.

Several tools for the prediction and the assessment of the structural behavior of masonry buildings have been developed in recent decades. Numerical tools have been favorably developed and preferred over analytical approaches, given the complex mechanical response of masonry and the irregular geometries of historic masonry buildings. In this chapter, a thorough review of numerical strategies for the analysis of masonry structures is presented. Additionally, classification of these strategies is also suggested to logically organize the extensive literature on this topic. Even though a wholly congruent categorization of all the numerical tools is essentially unrealistic given the specific aspects of each solution developed, the existing numerical strategies are subdivided into four classes: block-based models, continuum models, geometry-based models, and macroelement models. Each class is thoroughly reviewed and the open challenges in numerical modeling of masonry structures are critically examined.

In this paper, a damaging block-based model is proposed for the numerical analysis of the cyclic behaviour of full-scale masonry structures. Solid 3D finite elements governed by a plastic-damage constitutive law in tension and compression are used to model the blocks, while a cohesive-frictional contact-based formulation is developed to simulate their cyclic interaction. The use of tests on small-scale specimens to calibrate the mechanical properties of the numerical model is presented and discussed. The tests belong to a comprehensive experimental campaign performed on calcium silicate brick masonry. The calibrated models are used to simulate in-plane and out-of-plane cyclic tests on masonry walls made of the same material, as well as a quasi-static cyclic pushover test on a full-scale terraced masonry house. The efficiency, the potentialities and the accuracy of the model here proposed are shown and discussed. The capability of explicitly representing structural details (e.g. running bonds) and any in-plane and through-thickness texture of masonry, which appears essential to study the response of masonry structures, is guaranteed by the block-based modelling approach. A good agreement between the numerical results and the experimental outcomes is observed. This allows to validate the model in the cyclic response as well as the strategy proposed for its mechanical characterization.