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.

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.

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.

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.

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.

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.

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.

Post-earthquake structural damage shows that out-of-plane (OOP) wall collapse is one of the most common failure mechanisms in unreinforced masonry (URM) buildings. This issue is particularly critical in Groningen, a province located in the northern part of the Netherlands, where low-intensity induced earthquakes have become an uprising problem in recent years. The majority of buildings in this area are constructed using URM and were not designed to withstand earthquakes, as the area had never been affected by tectonic seismic activity before. OOP failure in URM structures often stems from poor connections between structural elements, resulting in insufficient restraint to the URM walls. Therefore, investigating the mechanical behaviour of these connections is of prime importance for mitigating damages and collapses in URM structures. This paper presents the results of an experimental campaign conducted on timber joist-masonry cavity wall connections. The specimens consisted of timber joists pocketed into masonry wallets. The campaign aimed at providing a better understanding and characterisation of the cyclic axial behaviour of these connections. Both as-built and strengthened conditions were considered, with different variations, including two tie distributions, two pre-compression levels, two different as-built connections, and one strengthening solution. The experimental findings underscored that incorporating retrofitting bars not only restores the system's initial capacity but also guarantees deformation compatibility between the wall and the joist. This effectively enhances the overall deformation capacity and ductility of the timber joist-cavity wall system.

Masonry structures, integral components of architectural heritage, are diffuse worldwide and continue to be interwoven within modern infrastructures. The complex nature of their constituents has driven active research toward understanding their mechanical behavior. Accurately and robustly representing the nature of masonry constituents is essential for structural analysis, design, and preservation tasks. This study adopts an adjustable contact constitutive model recently proposed to simulate bond behavior in masonry assemblages subjected to in-plane shear-compression loading. The adopted contact constitutive model, recently proposed by the authors within the Distinct Element Method (DEM) framework, addresses the intricate behavior of unit-mortar interfaces by employing a piecewise linear softening function controlled by the user to capture the softening regime in tension and shear. Meanwhile, the compressive region of the masonry interfaces is controlled by a compressive cap with a radial return algorithm under the explicit time-marching integration scheme of DEM to implicitly couple the shear and compressive behavior. The performance of the constitutive model was assessed on a set of calcium silicate wall experiments tested under in-plane shear and compression loading and presented a comprehensive variety of failure modes. The experimental and numerical results are compared on each system’s global and local behaviors. The findings underscore the robustness of the proposed contact constitutive model in accurately capturing the complex mechanical response of masonry and highlight its potential for structural analysis and damage prediction of a diverse spectrum of masonry structures.

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.

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.

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.

Cracks represent a prevalent form of damage in masonry structures, posing not only aesthetic concerns but also compromising structural durability; therefore, they are undesirable and need to be repaired. The repointing technique is traditionally implemented in this context, especially in historical masonry. However, this method fails to provide a long-term solution, leaving structures vulnerable to future damage. The paper investigates the applicability of a bio-based self-healing mortar to enable autonomous repair of masonry. This innovative mortar, developed to repair concrete structures, was implemented to explore the capacity of couplets to recover their original bond capacity and aesthetic aspect after multiple damaging events. Specimens built with calciumsilicate and clay bricks were subjected to subsequent cracking cycles using a crack-mouth-opening -displacement controlled bond-wrench test. Experimental results showed that self-repair, in terms of bond restoration and aesthetic filling of cracks, occurs even after multiple cracking cycles when the bio-based mortar is used with both types of bricks, optimizing the autogenous healing (intrinsic) of cement-based mortars. The effectiveness varied also according to the types of brick and healing environment used, e.g. under humid conditions (RH ~ 95%), 50% vs 80% of the original capacity was regained in fully separated couplets made respectively with clay and calcium-silicate bricks.

This study presents a robust contact constitutive model in the distinct element method (DEM) framework for simulating the mechanical behavior of masonry structures. The model is developed within the block-based modeling strategy, where the masonry unit is modeled as deformable blocks with potential crack surfaces in the middle of the bricks, while the mortar joints are defined as zero-thickness interfaces. The modeling strategy implements multi-surface plasticity with damage mechanics, including a tension cut-off, Coulomb failure criterion, and an elliptical compressive cap for the damage in tension, shear, and compression, respectively. Two new features are introduced in this contact model: a piecewise linear softening function for strength degradation in tension and shear and a hardening/softening function to phenomenologically define the compressive damage of masonry composite into the unit-mortar interface. The constitutive model is implemented in commercial DEM software using the small displacement configuration and validated against material and experimental tests on masonry walls subjected to constant pre-compression and monotonically increasing in-plane load. The experimental and numerical results regarding the force-displacement relationship and damage pattern produced by the proposed constitutive model are compared and critically discussed, demonstrating the capability of DEM coupled with the suitable constitutive law in simulating the behavior of masonry structures.

In the Netherlands, subsidence due to different causes is linked to damage to the ubiquitous masonry structures. Finite element (FE) analyses can be used to assess the response of the structures subjected to settlements. This paper presents the comparison between three-dimensional FE modelling strategies to investigate the response of an unreinforced masonry building on a strip foundation. The aim is to investigate whether different modelling approaches demonstrate consistent results. The soil-structure system is modelled employing two strategies: a coupled model, in which the structure is tied to the soil volume, and an uncoupled approach that divides the soil and structure into two sub-systems. Two displacement fields, imposed at the bottom of the soil volume, idealize various shapes of the subsidence troughs, with increasing intensity measured by their distortion. Non-linear interfaces are used to simulate the soil-foundation interaction, and their stiffness values vary based on the type of model. The displacements, interface stresses and crack patterns of the selected modelling strategies are consistent. The interface types do not influence the response of the façade, whereas the shape of the settlement does play a key role. The uncoupled models exhibit, on average, slightly higher values of damage than coupled models for a given imposed distortion. The two modelling strategies require almost the same computational time and show similar convergence. Because of the limited contribution of small soil volumes in uncoupled models, the superstructure sub-system can be directly utilized to assess the response of structures undergoing vertical displacements, thereby reducing the modelling burden.

One of the characteristic features of the city of Utrecht is its extensive system of canals and wharf cellars, whose constructions date back as early as the 1200s, and which are now considered as one of the historical properties of the city. A typical wharf cellar in Utrecht comprises a masonry barrel vault with multi-layered rings for the cellar interior, masonry piers which are interconnected to the other wharf cellars, and spandrel walls for the façades. Due to increased traffic volume and urbanization which caused the increase of dead load and traffic load, it is important to assess the structural safety and state of maintenance of these historical structures. In this paper, a novel safety assessment framework for these structures is presented and applied to the analysis of a typical masonry wharf cellar in central Utrecht. The geometry of the cellar is first parametrically generated, which is then used to create a block-based numerical model for analysis using the Distinct Element Method (DEM), where bricks units are modelled as discrete blocks separated by zero thickness interfaces. Traffic loads in accordance with the Dutch Standard traffic model for regular vehicles and emergency service vehicles are calculated and the dispersion through the filling soil is modelled. The ultimate load due to these load configurations is then assessed. The analysis results can be used to identify the critical load cases and the failure mechanisms of the wharf cellar, while also providing general insights into the safety and stability of the cellars, thus aiding engineers in their efforts to extend the lifespan of these historical structures.

This study aims to investigate the damage response of unreinforced masonry (URM) façades resting on strip foundations and subjected to ground settlements via numerical models. The models depict the non-linear constitutive behaviour of both the masonry, via smeared cracking, and of the soil-foundation interaction, via nonlinear interface elements. The influence of building features, such as the masonry material, the length over height (L/H) ratio of the geometry, the wall thickness, the number and size of openings and different types of strip foundations (i.e. reinforced concrete and unreinforced) is examined. A sensitivity study additionally investigates the influence of the interface stiffness and its constitutive model. A Gaussian curve is used to replicate the shape of the ground settlements; These simulate the loss of support underneath the foundation due to urban subsidence. Eight settlement shapes are applied in the FE models, including both symmetric and asymmetric profiles, while the angular distortion is used to measure their intensity. A new aspect is that the extent of the induced damage to the façade is assessed objectively using a damage parameter that represents the number, length and width of cracks in a single scalar value. The method distinguishes between the applied settlement profile at the bottom of the interface and the retrieved settlement profile measured on the façade. The analyses indicate that for a value of the angular distortion equal to 2 ‰ (or 1/500), computed from the resulting deformations of the façades, 60% of the models exhibit serviceability damage associated with cracks of about 5 mm width. Accordingly, the limit values available in the literature are observed to be too optimistic and not conservative in relation to the analyses presented in this study. A key outcome is that facades with an L/H smaller or equal to 1 do not exhibit cracks wider than 1 mm. Façades on reinforced concrete foundations were observed to be less susceptible to settlement damage, compared to unreinforced ones.