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.

Simulating the seismic behaviour of unreinforced masonry (URM) is challenging due to large deformations and severe damage. Capturing this highly nonlinear response requires advanced numerical modelling strategies that represent block separation, debonding, friction, and impact. Discontinuum-based modelling strategies, such as the Distinct Element Method (DEM), are well suited, as they explicitly represent bond failure and damage progression from cracking to collapse. DEM relies on the explicit time integration scheme of motion equations; hence, the choice of the damping scheme becomes critical. Typically, mass-proportional damping is used in dynamic analysis, often without complementing it with stiffness-proportional damping which requires unpractical reduction of the time steps to ensure numerical stability. Yet relying solely on mass-proportional damping can overdamp low frequencies and underdamp high frequencies. This study implements and validates an alternative damping approach, Maxwell damping, where multiple spring-dashpot elements are introduced at unit-mortar interfaces within a simplified micro-model. This work introduces an optimization algorithm to tune the Maxwell elements without heuristics, targeting near-uniform damping over a broad frequency range. Effectiveness is assessed against shake-table tests on a full-scale cross-vault URM specimen. Predicted displacements, accelerations, damage evolution, and computational efficiency is compared with mass-proportional and zero-viscous damping models. This study investigates Maxwell damping as a practical relaxation scheme for the seismic analysis of complex masonry systems using DEM, building on prior formulations in the literature and extending them to the present modelling and validation context.

An existing interface material model for quasi-brittle fracture, originally developed within the Discrete Element Method framework, is implemented and enhanced for use in implicit Finite Element analyses of unreinforced masonry structures. The model captures mixed-mode fracture in tension-shear and combines cohesion with Coulomb friction in compression-shear. To address convergence issues arising when loading–unloading takes place, due to a discontinuity in the traction–separation relation, a regularization of the frictional contribution is proposed. A new model parameter is introduced and a calibration procedure to ensure numerical robustness and objectivity is presented. Furthermore, the consistent tangent stiffness matrix is derived to improve convergence in full-scale simulations. The improved model is applied within a simplified micromodelling approach to simulate the in-plane cyclic response of 2D masonry structures, including a shear wall and a spandrel subjected to a combination of horizontal and vertical actions. The results demonstrate that the model accurately reproduces key aspects of masonry behaviour, including stiffness degradation, energy dissipation, and crack patterns, while maintaining robustness and efficiency in complex cyclic loading scenarios.

Terraced buildings with cavity walls are among the most common types of construction in the northern part of the Netherlands. Since 1980, the inner walls of these buildings have been constructed using either calcium silicate bricks (214 × 102 × 75 mm) with thick mortar joints (10 mm) or, more recently, calcium silicate blocks (437 × 198 × 100 mm) with thin mortar joints (3 mm). The shear properties of these units play a crucial role in the seismic response of buildings, particularly in regions like Groningen, which is prone to seismic activity due to artificial extraction. This study investigates the shear interface behavior of these two types of masonry units by testing multiple triplet samples under varying levels of normal stress at the interface. The results provide detailed insights into the shear properties of both brick and block masonry, offering valuable data for enhancing the accuracy of numerical simulations and predicting the structural capacity of these types of masonry buildings.

Masonry buildings in the Netherlands are especially prone to damage in the form of small cracks. This is because the masonry is unreinforced, the foundations are shallow and often also unreinforced, the bedding is composed of soft soils like peat or clay, dilation joints are missing in older or historical structures, and current loading conditions, such as earthquake vibrations, were never considered in the design of the buildings. The latter includes mining operations for salt and gas that have led to subsidence and induced seismicity. Moreover, farming policy and water management, in combination with regional subsidence, have led to varying groundwater table levels which, in turn, cause wetting and drying of sensitive soils. This process is exacerbated by more extreme seasons of precipitation and drought because of climate change, leading to swelling and compaction of the ground underneath buildings. To understand building damage in this context, it is necessary to evaluate the combined effects of these various hazards. Their actions can be decomposed into vibrations caused by earthquakes and ground deformations. The former can be characterized by the PGV or PGA of the vibrations, and the latter by the induced curvature of the soil surface and/or by the horizontal strains at the surface because of deformations deep in the underground. Moreover, repeated earthquake events and seasonal soil subsidence or heave lead to cyclic actions. The contribution and interaction of these loads causing progressive damage to masonry buildings have been the focus of an extensive modelling study with detailed non-linear models of the buildings and the soil. The slow soil deformations were analyzed first and served as the starting point for subsequent, repeated vibrations. For example, a horizontal strain of 0.1 mm/m caused by mining, in combination with an angular distortion of 1/2000 due to local soil compaction, can produce cracks of about 1 to 2 mm wide in a particular masonry façade. The damage is then aggravated by an earthquake vibration in the order of 5 mm/s, which is further increased by about 10% with a repeated event. The expected final damage may include multiple cracks of up to 3 mm. In this manner, the combination of all actions can lead to the establishment of conservative thresholds to prevent or limit damage to existing structures.

Within the context of light damage to unreinforced masonry structures, recent tests have shown that the cracking behaviour of calcium-silicate brick masonry walls makes them more vulnerable to in-plane loads when compared against fired-clay brick walls. To further explore this observation, four nominallyidentical walls have been tested. Two of the specimens (3m wide and 2.7m tall) were built with calcium-silicate bricks and twowith fired-clay bricks. Additionally, two boundaries were compared: a top cantilever boundary, and a doubled-clamped configuration. The quasi-static, in-plane, two-way cyclic tests imposed small (0.03 to 0.1%), repeated drifts on the walls to investigate the initiation and propagation of small cracks. To monitor the cracking behaviour, high resolution Digital Image Correlation was applied. At the end of the tests, large drifts up to 2% were exerted to compare the near-collapse behaviour of the walls. The tests revealed that thewalls with the more restrictive boundary, deforming mostly in shear, behaved the stiffest and also developed cracks earlier than the cantilever walls. Additionally, this constraint also led to more vertical cracks that split bricks, while the cantilever walls saw more horizontal and diagonal cracks along mortar joints and at mortar-brick interfaces. While the calcium-silicate-proved to be more brittle than the fired-clay masonry for the cantilever test, the claymasonry exhibited similar brick-splitting cracks in the double-clamped configuration. In general, there were fewer but wider cracks in the calcium-silicate specimens, while the clay brick samples showed less localisation and more smeared-crack behaviour. In terms of stiffness, the calcium-silicate walls were initially stiffer and achieved a higher capacity. Moreover, these walls also presented a higher hysteresis associated with more frictional failures. In sum, while cracks on the calcium-silicate walls were confirmed to be more serious, their increased stiffness could lead to smaller drifts during dynamic loading, and the walls would develop less damage; this requires further study.

Soil heterogeneity, due to variations in the subsurface stratigraphy or properties within a layer, can trigger or amplify differential settlements that affect buildings and infrastructure and can thus lead to (increase in) damage. The state-of-the-art mainly focuses on the effect of heterogeneous properties within a layer on engineering problems. From this, it is known that the variation in properties can increase the vulnerability of a structure. However, nearly always variations in the soil lithological conditions are disregarded, while they can influence subsidence potentially even more. Lithological variations are relevant both at the scale of individual buildings as well as different scales (city, regional, country), for which often detailed soil information is not available. Thus, for a better prediction of potential building damage related to subsidence, knowledge about the scale and influence of lithological variations is needed. This paper describes an approach to quantify and investigate the influence of lithological heterogeneity at the scale of a single building. Moreover, this exploratory study evaluates the influence of lithological heterogeneity on the spatial variability of settlements, intending to upscale the approach to regional application. Two independent datasets at high resolution (site-specific) and low resolution (national level) are used to retrieve the stratigraphic conditions for the area selected for the analyses. One-, Two- and Three-dimensional numerical models, based on the collected information are used to simulate the consolidation process and settlement due to a uniform load imposed on the surface level of the study area. Additional analyses investigate the influence of loading conditions and groundwater table. The parameter “correlation length” is used to quantify the spatial variability of the soil layer thickness and then of the computed settlements. The analyses reveal that the spatial variability of the soil strata thickness matches that of the computed settlements, ranging from 2 to 10 meters. In other words, the lithological variability of the soil leads to differential settlements occurring at the scale of man-made structures such as houses, roads, and embankments. Thus, the results encourage including the contribution of lithological heterogeneity in models and predictions of differential settlement at the scale of individual structures. Moreover, the statistical properties, in terms of mean, spread and distribution shape, of the settlement computed through in-situ specific models, match with those derived at the national scale. These results are expected to support the identification of areas potentially influenced by lithological soil heterogeneity, thus showing potential for upscaling to regional or national levels.

Subsidence caused by natural or human-induced factors can occur unevenly, resulting in differential settlements. Existing unreinforced masonry (URM) buildings are susceptible to damage from differential settlements. However, the extent of the damage varies between structures, depending on factors such as the magnitude and pattern of the settlements, along with the features of the building and the properties of the underlying soil. Non-linear finite element analyses (NLFEA) are often used for studying the damage response, accounting for variability in soil and structural features. This study uses 6912 NLFEA, including 8 variations in façade geometry, 3 masonry materials, 2 soils, 2 shallow foundation systems, and 72 settlement patterns, to develop fragility curves for URM buildings undergoing subsidence. Old Dutch URM buildings with strip foundations are modelled using 2D plane-stress façade models, accounting for non-linear smeared shearing, cracking and crushing of masonry and 3D effects of transverse walls. Settlement troughs are applied at a non-linear soil-foundation interface, with angular distortion (β) progressively increasing to quantify settlement intensity and building deformation. As β increases, the NLFE models exhibit progressive cracking damage, with severity objectively assessed through the parameter Ψ considering crack width, length, and number. Then, the distortion β is used as the demand parameter to develop the fragility curves. The analysis shows that long façades are twice as likely to experience 5 mm cracks from settlement damage compared to short façades under an applied β of 2 ‰ (1/500). For this applied β, proposed as an acceptable limit for many structures in the Eurocode, half of the models exhibit cracks up to 5 mm wide. Therefore, while 1/500 may be considered safe for structural integrity, it can still lead to noticeable damage. Light damage occurs even at angular distortion values below 0.5 ‰ (1/2000), with 10 % of models showing cracks up to 1 mm wide.

Damage assessment for masonry structures subjected to settlement is crucial for ensuring structural safety, guiding repairs, and preserving the built environment. Non-linear finite element modelling offers an effective approach for this purpose, though balancing model complexity, computational cost, and predictive reliability remains a key challenge. This study addresses the absence of a systematic comparison between macro- and simplified micro-modelling strategies for such analyses, clarifying their respective strengths, limitations, and sensitivity to key parameters. The performance and accuracy of semi-coupled NLFEM models are compared in simulating the response of a 1/10th scaled masonry façade under settlement, available from prior research. The two approaches considered are: simplified micro-modelling, where bricks are represented as expanded blocks with non-linear interfaces for mortar joints and their contact edges, and macro-modelling, where masonry is homogenised into an equivalent orthotropic composite material. The macro-models employ two well-established constitutive models, the Total Strain Rotating Crack Model (TSRCM) and the Engineering Masonry Model (EMM), to capture the non-linear cracking behaviour of masonry. Sensitivity analyses assess the influence of base interface models and the interface’s tangential stiffness. The results show how the selection of the modelling approach depends on the analysis objective: The macro-model with the Engineering Masonry Model best predicts damage severity, deviating by only 10% from the experiment, further improved by calibrating the minimum head-joint tensile strength. While all models yield similar predictions for vertical displacements of the façade, the TSRCM better captures overall and horizontal displacements, whereas the simplified micro-model more accurately represents the crack pattern. The EMM-based macro-models are the most computationally efficient, with TSRCM requiring 1.5 times the CPU time of EMM, and the micro-model requiring twice as much. The analysis also shows that the TSRCM-based macro-model is more sensitive to variations in the type of base interface models and base interface tangential stiffness, convergence criteria, incremental-iterative procedure, and analysis settings, whereas the EMM macro-model and the simplified micro-model are less affected. By identifying the strengths and limitations of each modelling approach, this study supports informed modelling choices for a more reliable assessment of settlement damage, contributing to the effective protection of existing masonry structures.

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.

This study presents a semi-automated, data-informed framework for selecting parameter-consistent numerical models to approximate the in-plane behaviour of clay and calcium silicate masonry walls. A comprehensive experimental campaign has been executed on full-scale unreinforced calcium silicate and clay masonry walls at Delft University of Technology. The in-plane response of these walls was evaluated based on stiffness, strength, damage intensity at equivalent drift levels, and the overall impact of the damage. The findings indicate that unreinforced calcium silicate masonry walls are more prone to damage through the brick units, while cracks in unreinforced clay masonry walls predominantly align with mortar joints. Calcium silicate walls tend to develop larger and more prominent cracks, often requiring the replacement of individual bricks for a complete repair. In contrast, the damage in clay walls is typically easier to address through repointing of mortar joints. A parametric finite element analysis was performed to investigate these failure mechanisms, systematically varying input parameters to generate 3,456 numerical simulations. Each model permutation was evaluated to select models that closely approximate observed experimental responses. Unlike conventional calibration methods, this framework systematically explores possible combinations of input and output parameters to identify numerical models that replicate key structural behaviours. The preliminary results demonstrate that multiple parameter combinations can yield numerical responses closely matching experimental observations, providing a structured approach for improving masonry modelling practices.

Cycles of settlement and uplift beneath existing masonry structures can lead to visible cracks, which not only affect the aesthetic appearance and functionality of the building but can also compromise its structural integrity and undermine the occupants' sense of safety. These cyclic ground movements can be triggered by seasonal actions, such as fluctuation in the groundwater table. In the Netherlands, many existing masonry structures on shallow foundations rest directly on the subsurface, making them vulnerable to cyclic ground movements. Settlement and uplift cycles cause “breathing” masonry cracks, which open and close over time without fully sealing. This study uses finite element analyses to investigate and assess the damage of structures subjected to cyclic quasi-static ground movements. A case study is presented for the analysis, featuring the geometry of an existing low-rise masonry structure with an age exceeding 50 years. A 3D non-linear shell-element model is used to evaluate the structural response, featuring an unreinforced strip foundation and including the non-linear tensile softening and cracking behaviour of masonry. Heaving and sinking displacements are applied to a non-linear interface simulating the soil-foundation interaction at the bottom of the strip foundation. The intensity of the ground displacements is quantified by their angular distortion. A damage parameter objectively assesses the severity of damage by considering the number, length, and width of cracks. Results indicate that repeated cycles of settlement (and uplift) have been observed to cause irreversible cracking damage in the model, with crack widths ranging from 1 to 5 mm, progressively increasing over time. Damage occurring during settlement is, on average, twice as severe as that during uplift. Overall, cycles of settlement and uplift may induce cracking damage up to twice as high as that caused by cycles of settlement alone, depending on the magnitude and shape of the ground movements.

The integration of bacteria-based self-healing mortars has emerged as a promising solution to address repair due to recurring cracks and preserving masonry durability. Building upon a recent pilot study demonstrating the efficacy of a self-healing agent in the repair of masonry made with cement-based mortar, this follow-up study explores the potential of integrating the added-in healing agent in a pre-bagged cement-lime mortar - more commonly used in masonry applications. Through bond wrench tests and a 30-day healing period involving wet-dry cycles, the study evaluates aesthetic and flexural bond strength recovery of couplets built with solid clay bricks. Results showed that the addition of the agent altered the initial flexural bond strength, with bacteria-based masonry couplets four times stronger than the plain reference ones - without containing the agent. The mortar’s colorwas also affected. Additionally, bacteria-based specimens demonstrated automatic repair, restoring up to 33% of the original flexural bond strength, while referencemasonry couplets showed no evidence of autonomous healing. However, instances of leaching, possibly attributed to the agent’s substrate, prompted a revision of the strategy employed for the healing environment. Further research will specifically target the observed leaching issue by exploring the effects of multiple healing environments.

This study reviews existing research on the effects of the interaction between in-plane (IP) and out-of-plane (OOP) behaviors on the seismic response of non-framed unreinforced masonry (URM) structures. During earthquakes, masonry buildings exhibit complex behaviors. First, walls may experience simultaneous IP and OOP actions, or pre-existing IP and OOP damage, deformation, or loads that can alter their unidirectional IP or OOP seismic response. Second, the IP and OOP action of one wall can affect the behavior of its intersecting walls. However, the effects of these behaviors, referred to as “direct IP-OOP interactions” and “Flange effects”, respectively, are often disregarded in design and assessment provisions. To address this gap, this study explores findings from experimental and numerical research conducted at the wall level currently available in the literature, identifying the nature of these interaction effects and the key parameters that affect their extent. The available body of work includes only a few experimental studies on interaction effects, whereas numerical investigations are more extensive. However, most numerical studies focus on how OOP pre-damage/deformation influences the IP behaviors (OOP/IP interactions) and the role of flanges in IP response (F/IP interactions), leaving significant gaps in understanding the effects of IP pre-damage/deformation on the OOP response (IP/OOP interactions) and the OOP response in the presence of flanges (F/OOP interactions). Among the parameters studied, boundary conditions, wall height-to-length aspect ratio, and vertical overburden are found to have the most significant influence on interaction effects because of their relevance for the IP and OOP failure mechanisms. Other parameters, such as the restriction of top uplift, the presence of openings, or changes in slenderness ratio, are not comprehensively studied, and the available data are insufficient for definitive conclusions. Methodologies available in the literature for extrapolating the findings observed at the wall level to building-level analyses are reviewed. The current predictive equations primarily address the effects of OOP pre-load and Flange effects on IP response. Furthermore, only a few macro-element models are proposed for cost-effective, large-scale building simulations. To bridge these gaps, future research must expand experimental investigations, develop more comprehensive design and assessment equations, and refine numerical modeling techniques for building-level applications.

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.

Drift limits are useful thresholds; during design or retrofitting analyses, engineers can compare the expected behaviour of a structure to drift limits that predict when the structure will reach a certain condition. This helps ensure that structures satisfy specified performance goals when exposed to certain hazards. Masonry walls are susceptible to damage from lateral in-plane actions such as wind or earthquake loading; ensuring that in-plane drift remains sufficiently small will help limit this damage. Drift limits based on crack-based damage are scarce, however, with DS1 limits being extrapolated from higher damage grades based on structural strength capacity or ductility. In this work, crack-based damage is evaluated on a multitude of full-scale experimental walls surveyed with digital image correlation. This method observes the initiation and propagation of cracking. Cyclically incremental in-plane tests provide a range of drift-damage relationships. These are explored with machine learning to determine influential predictors and ultimately establish drift limits for light damage. Two types of brick masonry are explored: fired-clay and calcium-silicate. For the latter, light damage begins at an in-plane drift of 0.5 mm/m and can extend to 4.8 mm/m (or 0.48%) for the former before the masonry surpasses light damage and reaches structural damage grades. In comparison to drift limits set by other authors and (international) guidelines to characterise light damage, significant damage, or the ultimate capacity of masonry walls, the resulting drift limits for light damage from this work are set directly on the basis of experiments and are in good agreement with other authors. Most importantly, all the consulted values for ultimate capacity are much larger than the upper threshold for light damage determined herein, with limits for significant damage in the same order of magnitude. This result verifies the accuracy of the experimental crack-based characterisation used to establish the drift thresholds.

In this study, 2D and 3D modelling strategies are used to represent the behaviour of historical masonry buildings on strip foundations undergoing settlements. The application focuses on a two-story building, typical of the Dutch architectural heritage. An improved 2D modelling is presented: It includes the effect of the lateral walls to replicate the response of the detailed 3D models. The masonry strip foundation is modelled and supported by a no-tension interface, which represents the soil-foundation interaction. Two settlement configurations, hogging and sagging, are applied to the models, and their intensity is characterized using their angular distortion. The improved 2D model that includes the stiffness and weight of the lateral walls agrees in terms of displacements, stress and damage with the detailed 3D models. Conversely, the simplified 2D façade models without lateral walls exhibit different cracking, and damage from 2 to 7 times lower at an applied angular distortion of 2‰ (1/500). The improved 2D model requires less computational and modelling burden, resulting in analyses from 9 to 40 times faster than the 3D models. The results prove the importance of identifying and including the 3D effects that affect the response of structures subjected to settlements.

In the pursuit of introducing bacteria-based self-healing mortar for masonry repair, this study examined the potential of incorporating a poly-lactic acid (PLA) agent—already established in concrete repair—into cement-lime mortars, typical of historical constructions. Testing prisms constructed with varying lime/cement ratios revealed decreased flexural and compressive strength in high-cement-concentration mortars upon the addition of the agent; for mortars with high lime concentration, however, the agent led to an increase in both strengths. Furthermore, the agent's potential to self-repair was confirmed by allowing the remaining portions of tested samples to heal under humid conditions. Irrespective of mortar composition, cracks were resealed thus confirming the aesthetic, and potentially watertightness, restoration.

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.

The seismic assessment of the out-of-plane (OOP) behaviour of unreinforced masonry (URM) buildings is essential since the OOP is one of the primary collapse mechanisms in URM buildings. It is influenced by several parameters, including the poor connections between structural elements, a weakness highlighted by post-earthquake observations. The paper presents a mechanical model designed to predict the contributions of various resisting mechanisms to the strength capacity of timber-joist connections in masonry cavity walls. The research presented in this paper considers two different failure modes: joist-wall interface failure, and OOP rocking behaviour of the URM walls. Consequently, two mechanical models are introduced to examine these failure modes in timber-joist connections within masonry cavity walls. One model focuses on the joist-wall interface failure, adopting a Coulomb friction model for joist-sliding further extended to incorporate the arching effect. The other model investigates the OOP rocking failure mode of walls. The combined mechanical model has been validated against the outcomes of an earlier experimental campaign conducted by the authors. The considered model can accurately predict the peak capacity of the joist connection and successfully defines the contribution of each mechanism in terms of resistance at failure.