This paper investigates the response of one-way spanning unreinforced masonry (URM) walls first statically tilted in the in-plane (IP) and out-of-plane (OOP) directions and then subjected to seismic OOP loading, a subject largely overlooked in the literature. The study is motivated by this knowledge gap and its particular relevance to Netherlands, where ground settlement often leads to visible tilting in buildings, yet sufficient evidence for if and how such tilting should be explicitly considered in design and assessment does not exist. The numerical modeling approach previously proposed by the authors, validated against complex experimental data, is employed in a comprehensive parametric study to provide preliminary insights into the seismic response of tilted walls. The model represents URM unit-by-unit using nonlinear 3D solid expanded blocks and cohesive-frictional zero-thickness joints. Two wall specimens, one short and one long, are subjected to one level of IP base tilting and two levels of OOP base tilting. Static and dynamic OOP loading is then applied while maintaining the prescribed tilt. Under static OOP loading, three levels of vertical pre-compression are considered, representing conditions in low-rise residential buildings. For dynamic OOP analyses, a multi-step loading sequence with varying levels of overburden is used. The results show negligible sensitivity to IP tilting (even up to 4°). While the specimens exhibit slightly greater sensitivity to OOP tilting, primarily due to reduced vertical confinement and increased uplift, responses remain largely stable even with large OOP drift (up to 22% of wall thickness). Aside from the aforementioned findings, this study, being the first one in the literature studying load-bearing tilted walls, highlights key limitations which may have affected the outcomes and emphasizes the need for further research to better understand the behavior of tilted URM walls.

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.

This paper presents a numerical investigation on the effects of settlement-induced pre-damage on the seismic out-of-plane (OOP) response of two-way spanning non-framed unreinforced masonry (URM) walls, investigating also the suitability of static analysis procedures for simulating the dynamic OOP response of pre-damaged walls. For this purpose, the finite-element block-based modeling approach developed and validated by the authors in previous works is employed. URM walls with various geometries and boundary conditions are simulated to investigate the effects of openings and wall-to-diaphragm connections on pre-damage effects. Each specimen is subjected to various settlement profiles, and different levels of obtained settlement-induced damage states are used as initial conditions for OOP analyses. Static and dynamic OOP simulations, the latter considering both induced and tectonic seismicity, and modal analyses are performed. The outputs show that settlement effects on the OOP response emerged as early as the light pre-damage state. Sagging, previously considered in literature less damaging than hogging, caused the greatest OOP stiffness and strength reduction, up to 92% and 80%, respectively. Hogging led to a 60% stiffness and 30% strength drop, particularly in walls with openings. Induced seismicity did not lead to collapse. Static analyses accurately estimated OOP strength and failure mechanisms.

Extracting cores with diameters of 100 to 150 mm from masonry structures has emerged as a novel, less destructive method for assessing the mechanical properties of masonry units, particularly their compressive strength. Unlike traditional methods, such as using larger wallets, this approach requires less material and causes minimal damage to the original structure, which is critical when dealing with historical buildings. However, to obtain consistent and reliable results, certain parameters, specifically the dimensions of the core cap, must be carefully defined, as they significantly influence the overall behaviour of the samples. The study employs a detailed block-based modelling approach, incorporating zero-thickness cohesive elements at the brick-mortar interfaces. Additionally, tangential and normal contact interactions were defined between the cap and core components. The concrete damage plasticity (CDP) model, implemented in ABAQUS, has been adopted as the constitutive model to account for the nonlinear behaviour of brick, mortar, and cap. The results indicate that the length of the cap has a more pronounced effect on the sample’s mechanical behaviour than its height. Additionally, the study investigates the mechanical properties of the interface between the cap and the core, identifying friction and normal stiffness as critical factors. These findings provide valuable insights for optimizing the core capping process and improving the reliability of masonry mechanical property assessments, particularly in the preservation of historical structures.

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.

This study investigates the effects of differential support motions, caused by filtering effects due to the building response to earthquakes, on the one-way bending out-of-plane (OOP) behavior of unreinforced brick masonry walls, a factor often overlooked in seismic assessments. A high-fidelity block-based numerical model is used to simulate walls with varying slenderness ratios, precompression levels, and boundary conditions. Floor motions from shake-table tests on two-story masonry buildings with flexible and rigid attic diaphragms under induced and tectonic seismicity are applied at the top and base boundaries of the models as loading signals. Results show that differential motions between supports significantly influence OOP wall response, reducing the peak acceleration associated with signals to provide collapse while increasing displacement capacity. This effect is most pronounced in walls with lower-slenderness ratios, higher precompression, or constraints against uplift and rotation at the top, as differential loading disrupts vertical arching mechanisms that, otherwise, enhance stability under uniform boundary motions. Using only the base signal, a common simplification in seismic assessments fails to capture these differential effects. The results of the simulations are then examined to investigate the largest OOP displacement at which walls can regain stability under dynamic loading, calculating dynamic stability displacement thresholds and showing an average dynamic-to-static stability ratio of 62%, consistent with the 60% ratio used in safety standards. However, deviations occur in walls with failure mechanisms differing from typical flexural behavior. The findings provide critical insights for more accurate seismic assessment and retrofitting of masonry walls by highlighting the importance of considering differential motions. Additionally, this study offers supporting data for the dynamic stability displacement thresholds currently adopted in seismic assessment guidelines, addressing a gap in experimental data and improving the reliability of safety evaluations for unreinforced masonry structures under seismic loading.

Historical masonry façades are susceptible to variations in temperature. This is because their movements—expansion caused by an increase in temperature or contraction by a decrease—are restrained by other structural elements. To analyse these effects, models typically assign a prescribed strain to the façade while enforcing a rigid boundary at the foundation (or the floors, if they are rigid). More advanced models include the foundation, with a stiffness different from that of the façade and no prescribed strain, as the restraining element. This leads to conservative estimations of damage since the restraining effect is large. Indeed, these models can be further improved. A temperature gradient across the façade, including the foundation, can produce more gradual strains in the material and thus less damage. For this study, the improvements consider the inclusion of the soil underneath the building. A realistic temperature gradient for a sunny summer day or a chilly winter night, including a gradient over the foundation and into the soil, is applied. The restraining effects are provided by the soil and the temperature gradients. In this manner, the consequences of temperature variations on clay-brick masonry façades are investigated. The models reveal that damage, observed as cracking in the non-linear masonry model, is significantly reduced when applying the more gradual temperature profiles. Moreover, the damage patterns observed are different from those obtained from a simpler model. This is an important observation since crack patterns are sometimes employed to determine the origin of the damage. Furthermore, the type of soil also plays a role in the intensity of damage observed for identical temperature profiles. Softer soils, such as clay, peat, or loam, provide less restraint than stiffer soils like sand. Hence, façades on softer soils are less likely to develop damage from temperature variations.

Historical buildings in the Netherlands are often founded on shallow, unreinforced foundations atop soft soils such as peat, clay, or loam, making them vulnerable to ground movements. These movements can result from autonomous settlements due to the building’s own weight, or from changes in the soil related to water table variations. Such sources typically induce differential vertical displacements, expressed as ground surface curvature. Movements from deeper sources, such as mining or tunnelling, also cause horizontal displacements or surface strains.

Masonry buildings are sensitive to strains from restrained shrinkage, temperature fluctuations, and soil movements. This study examines façade damage due to a combination of curvature and horizontal strain imposed through the foundations. Non-linear models of masonry façades were placed on a deformable soil block, whose boundaries were manipulated to create targeted combinations of curvature and strain at the surface.

The analysis of various combinations showed that while curvature and horizontal strain each cause damage—manifested as cracks in the masonry—their combination amplifies it. For instance, cracks 1 mm wide appear at a tensile strain of 5e−4 (0.5 mm/m), but when combined with an angular distortion of 1e−3 rad, only half that strain is needed to produce similar damage.

Understanding how curvature and strain interact to damage façades helps define safer deformation limits for vulnerable historical buildings, particularly in areas affected by water table regulation or mining. Additionally, the initial condition of structures must be considered when evaluating their vulnerability to external hazards, including seismic activity.

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.

Temperature variations in masonry façades can induce expansion and contraction movements. When these movements are restrained, cracking and material degradation may occur, especially in older buildings lacking movement or expansion joints. Such temperature variations arise from factors as solar radiation, shading, material color, reflectivity, and environmental conditions. This study investigates the magnitude and spatial distribution of surface temperature variations (ΔT) on exterior masonry wall surfaces using outdoor infrared (IR) thermography. A better understanding of the magnitude and distribution of ΔT is essential for accurate damage assessment and for improving the attributability of observed damage to temperature effects rather than to other causes. Field data were collected in Delft, the Netherlands. Thermal images were captured with an IR camera to identify temperature differences across various points on exterior wall surfaces under direct solar radiation and varying shading conditions. The acquired imagery was analyzed using temperature histograms and profiles to quantify thermal gradients over the surface area of the façades. Results revealed significant spatial temperature variations, with measured ΔT values reaching up to 13 °C between the warmest and coolest zones on individual façades. Even where façades showed no pronounced surface gradients, temperature differences of up to 6 °C occurred between different, contiguous exterior walls of the same building. The study demonstrates that outdoor thermography, combined with targeted image processing, effectively identifies thermal gradients on masonry façades. These gradients reflect uneven thermal responses under real environmental conditions, which can accelerate moisture-related damage, cracking, and material fatigue. The findings emphasize the need to account for surface temperature heterogeneity in damage assessment of existing structures.

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.

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.

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.

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.

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.

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.

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.

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.

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.