This paper presents a framework for developing fragility curves for masonry buildings on strip foundations exposed to subsidence using non-linear finite element (NLFE) analyses. A 2D plane-stress model of a masonry façade is used to evaluate the probability of cracking damage resulting from settlements. The model simulates the behaviour of typical Dutch two-storey historical buildings, using an established modelling approach to represent the non-linear behaviour of the façade, the transversal walls and the strip foundation, supported by a base interface for soil-foundation interaction. Settlements are imposed at the bottom of the interface, characterizing their intensity with the angular distortion. The damage severity is objectively quantified using the scalar parameter Ψ, computed considering the number, length, and width of the cracks. Cumulative probability functions are derived from 864 numerical analyses that account for realistic variations in building and soil features, including 3 masonry materials, 2 strip foundation systems, 2 interface soil materials and the 72 possible settlement patterns. The effect of each selected variation is evaluated individually. The proposed curves reveal a probability of over 25% for cracks up to 5 mm in width when the angular distortion equal to 0.2% (or 1/500), the threshold deemed acceptable by international codes, is applied to the models. Doubling the applied angular distortion results in an approximate doubling of the probability of damage. While the proposed curves are specific to the selected geometry, the framework can be adapted to accommodate different façade geometries, enabling the development of more comprehensive fragility functions.

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.

The seismic vulnerability of historical masonry structures has been extensively studied, with efforts primarily focused on assessing their earthquake resistance. However, such studies often consider these structures in isolation, disregarding their urban context. In densely built environments, the collapse of adjacent buildings during an earthquake can have a devastating impact on nearby heritage structures, even if they are inherently capable of withstanding seismic loads. On February 6, 2023, two major earthquakes, with magnitudes of Mw 7.7 and Mw 7.6, occurred nine hours apart, affecting the southeastern region of Türkiye. Post-earthquake site investigations revealed that the collapse of the historical Adıyaman Grand Mosque was likely triggered by the failure of a substandard reinforced concrete building in close proximity. This paper aims to investigate the failure mechanism of the Adıyaman Grand Mosque in a broader context. Preliminary study highlights the importance of conducting an extended analysis for heritage structures in urban environments, for reasons such as: (i) the complex interactions between buildings in densely populated areas during earthquakes, (ii) the detrimental effect of the failure of a nearby building on heritage structures, and (iii) the development of more effective mitigation strategies to protect and preserve heritage structures in such environments.

Temperature effects are frequently cited as the cause of light cracking in masonry façades, yet most modelling studies idealise thermal loading as uniform steps and represent restraint as fully fixed, assumptions that tend to exaggerate damage. This work evaluates whether realistic, non-uniform temperature gradients, like those produced by shading and insolation, together with soil–structure interaction as the dominant restraint mechanism, can generate cracking patterns consistent with field observations. A coupled thermo-mechanical FEM model with a homogenised masonry continuum and tensile softening is employed; the façade–foundation–soil system is modelled explicitly, and damage is quantified using a crack-based index Ψ. A parametric campaign (1200 simulations) spans two façade typologies (clay masonry on unreinforced masonry foundations; calcium-silicate on reinforced concrete strips), three layered soils, 33 geometries, and multiple vertical and two-dimensional gradient shapes. The results indicate that gradient shape is decisive: widely distributed vertical gradients trigger visible damage (Ψ≥1) at roughly half the temperature differential required by more localised gradients, with visible damage becoming likely around ΔT≈20 °C (warming) and ≈25 °C (cooling) for the most adverse shapes. Restraint stiffness governs severity: stiffer sandy profiles increase tensile stresses and cracking, whereas softer profiles accommodate thermal movement; relative to uniform, fully restrained models, crack initiation is delayed by ∼15–20 °C and cracking is less distributed. Geometric discontinuities also dominate sensitivity: larger/more openings and low vertical-masonry ratios promote earlier localisation, while overall length/height is secondary. Fragility-like curves provide thresholds useful for assessment and mitigation.

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.

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.

The structural response of masonry walls during flood events is a critical concern for the flood resilience of (Dutch) buildings, as they typically constitute part of the load-bearing structure. This study investigates the out-of-plane behaviour of a full-scale single-wythe fired-clay-brick masonry wall under out-of-plane hydrostatic pressure and debris impact loads. Experimental tests were conducted on a 2.7 × 2.7 m masonry wall subjected to a vertical pre-compression and simultaneously varying water levels and debris impacts at the Flood Proof Holland facility in Delft, the Netherlands. Results demonstrated that the wall remained within the linear-elastic regime up to a water depth of approximately 90 cm when the interior side was dry. Beyond this threshold, crack initiation and stress redistribution occurred, leading to significant deformation. On the basis of calibrated models, failure was predicted at approximately 150 cm water depth for a fully restrained wall. Debris impact tests showed that soft debris, represented by a floating log, caused negligible additional damage, whereas repeated impacts with a steel cube (hard debris) resulted in progressive cracking and local failure, particularly at higher water levels. Numerical models, including analytical, linear-elastic finite element method (FEM), and non-linear FE approaches, were calibrated using the experimental data. While one-way bending models predicted conservative failure thresholds, two-way, non-linear models accurately captured the wall’s deformation and cracking behaviour, demonstrating the importance of lateral boundary constraints in determining wall capacity and stability. The findings emphasise that traditional masonry walls in Dutch buildings can safely withstand water depths up to 90 cm without significant damage. However, higher water levels or hard debris impacts pose substantial risks, highlighting the need for improved flood resilience strategies. Future work should focus on cavity wall systems, leakage effects, and the behaviour of walls with openings.