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 cyclic joint constitutive model within a Distinct Element Method framework to simulate the in-plane response of unreinforced masonry structures. The model combines multi-surface failure criteria, including tensile cut-off, Coulomb friction, and an elliptical compression cap. It incorporates exponential softening, a unified damage scalar for stiffness degradation, and a hardening–softening law for compression. Shear-induced dilatancy is captured via an uplift-correction mechanism with an exponential dilatancy-decay law, while stiffness degradation governs energy dissipation. The model is validated at both material and structural scales. Material-level simulations of cyclic compression and shear tests show close agreement with experimental data. Structural-scale validation on full-height calcium-silicate walls under combined compression and cyclic lateral loading demonstrates the ability to reproduce rocking-dominated, shear-dominated, and hybrid failure mechanisms. The model successfully replicated global hysteretic force–drift loops, capturing stiffness decay and energy dissipation, as well as local failures like cracking, sliding, and toe crushing. The model also reproduced the drift-dependent transition from rocking to friction-controlled sliding, a key mechanism for earthquake assessment. By integrating these features into a single, efficient framework, the proposed constitutive model provides a robust tool for evaluating seismic performance and conserving heritage.

Low-rise masonry buildings worldwide frequently feature unreinforced masonry (URM) walls coupled with various pitched roof configurations supported by masonry gables. Past earthquakes have highlighted the vulnerability of these components to out-of-plane seismic loads due to their high slenderness, insufficient roof connections, and exposure to amplified accelerations while being subjected to minimal overburden due to their location at the upper part of buildings. This study presents key insights from the experimental campaign of the ERIES-SUPREME project, aimed at enhancing the understanding of the out-of-plane seismic behavior of masonry gables. Incremental dynamic tests were performed on three full-scale URM gables, simulating both induced and tectonic earthquake scenarios until collapse, using two shake tables. Differential motions at the top and bottom tables reproduced the interaction of the gables with three different roof diaphragm configurations, each introducing a unique filtering effect on the seismic input. The outcomes of the experiments can be used for refining existing numerical modelling strategies as well as contribute to developing improved tools for the seismic assessment of URM gables.

This article presents a dataset from an experimental campaign investigating the out-of-plane (OOP) seismic response of unreinforced masonry (URM) gables in existing buildings. Addressing a critical gap in published research, the dataset provides novel experimental data on the incremental dynamic OOP behavior of three URM gables tested under seismic loading until full collapse. All three gables were nominally identical but differed in their interaction with the supporting roof structure. This interaction was experimentally reproduced by imposing differential motions at the top of the gables, which were either linearly amplified or both amplified and phase-shifted relative to the motion at the base. This approach ensured idealized and numerically replicable boundary conditions, making the dataset an ideal benchmark for refining existing and developing new modeling approaches for URM structures. The dataset includes measured and calculated acceleration, displacement, and force time histories. Beyond supporting the validation and development of numerical models, it can also contribute to improving guidelines for the out-of-plane seismic assessment of URM gables and is openly available for further research and engineering applications.

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.

Damage and collapse of walls in the out-of-plane (OOP) direction are common failure modes in existing unreinforced masonry (URM) buildings when subjected to seismic excitation. These localized mechanisms also hinder the realisation of the complete in-plane seismic capacity of URM buildings. Among such OOP failures, a distinction can be made between (i) one-way bending which occurs in long walls and walls without side supports, and (ii) two-way bending which occurs in walls that have at least one vertical and one horizontal edge supported. This paper examines the suitability of a single-degree-of-freedom model for modelling the dynamic behaviour of URM walls subjected to OOP seismic excitation and undergoing two-way bending. The model operates in two phases: (i) initial elastic and (ii) post cracking, transitioning instantaneously between the phases once the force required to crack the wall is surpassed. Post cracking, the wall is treated as a system comprised of rigid blocks, and wall resistance is computed by combining three distinct contributions. These contributions are (i) bilinear elastic rigid block rocking, (ii) elastoplastic friction, and (iii) bilinear degrading component taking into account strength and stiffness degradation of walls. The model's complete behaviour in both phases is described by six independent parameters, which can be computed analytically. This paper explores the performance of the proposed model, especially when compared with and calibrated against experimental results from incremental dynamic testing of full-scale single leaf and cavity walls, for which the model demonstrates excellent agreement.

Unreinforced masonry buildings show high vulnerability to seismic loading, especially in the out-of-plane direction. Two-way spanning walls are characterized by effective restraints at at least one lateral side of the wall. Their seismic performance under out-of-plane loading has been studied in the literature for walls without openings or with one opening, but it lacks understanding in case of multiple openings. This study presents an engineering approach to calculate the out-of-plane capacity of two-way spanning walls with two openings. Five wall configurations were analysed via non-linear pushover analyses, and crack-pattern evolution tracked. A methodology was proposed which involves dividing the wall into panels whose performance is assessed separately. The division is based on the crack propagation observed in the numerical simulations. Two panels are defined as the wall portions comprised between a side support and an opening which are classified and analysed as three-sided supported walls. Another component corresponds to the wall portion between the two openings and is analysed as a one-way spanning wall. The assessment of the individual panels is based on formulations provided in the Dutch guidelines NPR-9998:2020 which show that the one-way spanning wall panel is the governing one, which is further proved by the analytical calculations.

Historical quay walls, constructed in unreinforced masonry, play a crucial role in the infrastructure of many Dutch cities. Designed originally as gravity retaining walls, these structures are increasingly subjected to traffic loads due to vehicles operating on roads built on their backfill. This study conducts a preliminary numerical evaluation of a strengthening technique aimed at prolonging the service life of such quay walls, focusing on a specific case in Amsterdam. The strengthening method involves drilling tubular steel piles through the existing masonry to anchor into a stable soil layer, with the piles bonded to the masonry using low-shrinkage casting concrete. The assessment models the interaction between the strengthening technique and the existing quay structures, including a detailed simulation of the installation process, identified as critical for proper simulation of the structural behaviour. While the technique significantly enhances the quay's force capacity, an improvement in displacement capacity was not evident, highlighting the need for further investigation.