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 study examines the influence of in-plane (IP) pre-deformations and -damages on the two-way bending out-of-plane (OOP) seismic response of non-framed unreinforced masonry (URM) walls. IP and OOP behaviors of non-framed URM walls are often studied individually and their interaction, such as the effects studied here, remains insufficiently explored. Hence, current design and assessment techniques of non-framed URM walls do not consider the effects of pre-damage and pre-deformation, overestimating safety. This paper addresses this gap. First, a simplified micro-scale numerical modeling approach is developed within Finite Element framework using expanded blocks and zero-thickness interface elements. Shell elements are adopted instead of solid blocks, which are traditionally more common in such studies, to enhance computational efficiency for extensive explorations. Second, the approach is validated against wall IP and OOP experiments, showing good accuracy and reliability. Third, the effects of IP pre-damage and pre-deformation on two-way OOP bending strength and stiffness, called IP/OOP interaction effects, are investigated in a parametric study. The effects of wall openings, IP boundary conditions, vertical pre-compression, and horizontal confinement on interaction effects are investigated. OOP loading is performed at different IP performance states identified via a crack-based approach. According to the results, IP pre-damage or pre-deformation reduced OOP strength between 0% and 30% and OOP stiffness between 30% and 50% for the walls studied in this research and representative of Dutch calcium silicate masonry, emphasizing the importance of accounting for IP/OOP interactions in seismic design and assessment of URM walls. Vertical pre-compression and horizontal confinement are identified as most influential parameters due to their effect on arching mechanisms. Existing analytical models, typically developed for one-way spanning walls, significantly overestimate the loss of OOP performance due to pre-deformation or pre-damage in two-way spanning walls. The study establishes a foundation for structured future research into IP/OOP interaction.

This paper investigates settlement-induced damages in unreinforced masonry (URM) walls using a high-fidelity block-based numerical modeling approach. The research aims to address gaps in the understanding of settlement effects on URM walls with flanges, particularly with respect to their seismic out-of-plane (OOP) behavior. A parametric study is conducted on four wall specimens with varying geometries, boundary conditions, and settlement scenarios, including symmetric and asymmetric patterns. The numerical models are developed via a high-fidelity block-based finite element method that simulates masonry using expanded blocks connected by zero-thickness joints, allowing for detailed analysis of cracking patterns and damage mechanisms. Different damage states, from no visible cracks to near-collapse conditions, are identified in the response of the walls and are used as initial conditions for subsequent monotonic static pushover OOP loading. The results highlight the significant influence of settlement-induced pre-damages on the OOP response of URM walls, with varying degrees of impact observed across different specimen configurations. The findings underscore the importance of considering even “light” settlement-induced pre-damages when assessing the seismic performance of URM structures, particularly in subsidence-prone regions. Under symmetric hogging, such pre-damage level can reduce OOP stiffness and peak strength by up to 41% and 20%, respectively. This study lays the groundwork for future investigations into the seismic behavior of pre-damaged masonry structures under dynamic loading and offers valuable insights for the development of more accurate assessment and mitigation strategies for buildings subjected to settlement deformations.

This paper presents a modeling approach for high-fidelity blind-prediction of dynamic responses of 3D-printed masonry-like structures, as part of a contest organized by Pacific Earthquake Research Center (PEER) for simulating shake table tests on 29 identical ⨅-shaped 1:15-scaled sand-based 3D-printed specimens, each subjected to a different earthquake. The contest challenged participants to predict experimental outcomes without access to test results. Leveraging their modeling approach originally developed for regular masonry, the authors proposed an innovative methodology to simulate these structures, implementing extensions to overcome challenges such as representing their continuum nature within a discrete block-and-joint framework and simulating their small-scale response via 1:1-scale counterparts. The numerical model blind-predicted the experimental outcomes with highest accuracy among participants. Parametric studies, before and after access to modal characteristics, showed the importance of such information for simulation accuracy, and the ability of the approach to investigate variability of dynamic responses in complement to physical tests.

This paper presents a comprehensive review of the effects of interactions between in-plane (IP) and out-of-plane (OOP) behaviors, referred to as IP-OOP interactions, on the seismic behavior of framed unreinforced masonry structures, consolidating findings from experimental, numerical, and analytical studies available in the literature. While masonry structures are highly vulnerable to seismic loading and undergo multi-directional seismic actions, most existing research focuses on their response to unidirectional forces, overlooking the complex interaction effects observed during real earthquakes. Moreover, although design and assessment standards acknowledge these interactions, they offer limited prescriptive guidance. The literature predominantly addresses the impact of IP pre-damage on OOP strength and stability (IP/OOP interaction), with comparatively fewer studies examining the reverse scenario, i.e., OOP pre-loading affecting IP resistance (OOP/IP interaction). Experimental data remains scarce, particularly for multi-bay frames and walls with openings, limiting the generalizability of current findings. Numerical simulations have significantly advanced the understanding of these interactions, yet their reliability relies on proper calibration against benchmark experiments, which are still limited in number. Among the most influential parameters affecting the effect of IP pre-damage on the OOP response, the height-to-thickness slenderness ratio plays a dominant role. Slender walls are especially prone to severe OOP strength degradation due to reduced arching action and increased instability. The length-to-height aspect ratio also influences failure modes under IP/OOP interaction, particularly in short walls where horizontal arching action reduces. Other critical factors, such as masonry material properties, boundary conditions, and frame stiffness, have been identified, but their effects remain less systematically studied. Analytical approaches have primarily focused on IP/OOP interaction effects. However, existing equations are often derived from limited datasets, restricting their predictive capabilities. The equation widely adopted in seismic guidelines has been shown to overestimate OOP strength reduction, underscoring the need for more refined models that incorporate broader experimental and numerical data. Future research should address these gaps by expanding experimental campaigns, enhancing numerical methodologies, and refining analytical frameworks to better represent real-world conditions.

This study deals with the high-fidelity block-based finite element simulation of dynamic out-of-plane (OOP) responses of unreinforced masonry (URM) walls, explicitly focusing on two-way bending behaviors under seismic loads, which is a common critical failure mode in real-world masonry structures. While experimental shake-table tests provide valuable insights into these behaviors, their high costs, complexity, and limited scalability highlight the need for advanced numerical modeling approaches. A state-of-the-art block-based finite element modeling strategy that conceives masonry as an assemblage of 3D damaging blocks interacting via contact-based cohesive-frictional zero-thickness interfaces, previously proposed for simulating cyclic quasi-static and dynamic one-way bending tests, is here extended for the first time to the simulation of incremental dynamic shake-table tests on OOP two-way spanning URM full-scale walls, subjected to a sequence of dynamic loads. The numerical models track the reference experimental behaviors with high accuracy in terms of collapse onset, failure mechanism, experienced acceleration and displacements, and hysteretic response. The effects of variations in mechanical properties, boundary conditions, and damping on the dynamic response are explored in a sensitivity study. The results indicate that slight changes in these parameters can lead to considerable differences in outcomes. This highlights the chaotic nature of the dynamic response of masonry walls, especially in near-collapse conditions, which makes probabilistic approaches more suitable for predicting masonry OOP dynamics. The proposed numerical methodology appears compatible with statistical frameworks, given the limited costs with respect to experimental tests, and it extends knowledge beyond physical experiments.

In this paper, a numerical procedure is proposed to simulate the dynamic out-of-plane response of unreinforced masonry (URM) walls. A state-of-the-art damaging block-based model, originally developed for quasi-static simulations, is extended for the first time in a dynamic regime. The blocks are represented using solid 3D finite elements governed by a plastic-damage constitutive law for both tension and compression. A cohesive-frictional contact-based formulation is used to account for interactions between the blocks. A simplified mechanical characterization is formulated to improve efficiency in wall-level analyses. Dynamic simulation is performed using a generalized HHT-α direct integration implicit solver and by implementing Rayleigh damping in the bulk. Such consideration allows the use of both mass and stiffness proportional terms of the Rayleigh damping without compromising efficiency. The strategy is applied to simulate incremental dynamic experiments performed on full-scale walls, showing good agreement between numerical and experimental results. The calibrated numerical model is then optimized to reduce computational effort while maintaining accuracy. The optimized model is used to investigate the effect of relative support motion on the one-way bending out-of-plane seismic response of URM walls, demonstrating the potential of the modeling strategy to explore the effect of boundary conditions that occur in real buildings but are often overlooked in laboratory experiments. This investigation also explores the adequacy of simplifications in capturing the effect of relative support motion, which can be adopted for simple modeling strategies commonly used in standard engineering practice.