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.@en

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.

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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.

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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.@en

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.@en

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.

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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.

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Sequentially Linear Analysis (SLA), an event-by-event solution strategy in which a sequence of scaled linear analyses with decreasing secant stiffness is performed, representing local damage increments; is a robust alternative to nonlinear finite element analysis of quasi-brittle structures. Since it is based on a fixed smeared crack constitutive model, severe spurious stresses and inaccuracies may develop due to misalignment of the crack with the principal stress directions. To this end, the elastic-brittle fraction model was conceived. The model separates the continuum into several parallel fractions or layers, each with different properties, chosen in order to represent the overall constitutive softening behaviour as accurately as possible. The main idea is to mimick a rotating crack by a superposition of fractions, each with a fixed crack direction. In this article, the model is presented for both the 2-dimensional and 3-dimensional frameworks, with a general transition from any saw-tooth law to fraction material properties. The fraction models are then validated and compared against the fixed crack model with SLA: using single element and structural case studies. It is shown that the fraction model is able to mimick the rotating crack model, that it leads to lesser spurious cracks and narrower localisation bands, and in turn results in a more flexible post-peak response over all case studies compared to the fixed crack model.

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This paper demonstrates the use of non-linear finite element modelling to investigate the response of structures subjected to different shapes of subsidence-related ground settlements. The approach is presented with reference to a two-storey unreinforced masonry façade resting on a shallow foundation. Eight realistic settlement shapes, based on field and literature data, are applied in the model with increasing intensity. The intensity of the subsidence profiles is characterized using their (angular) distortion. The extent of the induced damage on the façade is objectively and directly quantified by a damage parameter, based on the number of cracks, their length and opening. The performance of different settlement indicators and corresponding limiting values, typically employed in the state of the art, is in this paper discussed in relation to the damage modelling strategy; these are observed to be dependent on the shape of the settlement profiles. The aim of this paper is thus to provide insight into the extent to which the vulnerability of masonry buildings depends on the shape of the subsidence pattern and may serve as a warning not to use (deterministic) damage indicators such as angular distortion without considering the settlement shape.@en

Cracks are one of the most common expressions of damage in masonry structures. Aside from aesthetic issues, they can compromise the overall behaviour of the structure; therefore, they are undesirable and need to be repaired. The repointing technique is traditionally implemented in this context, especially in historical masonry. Nevertheless, future damage is not prevented and may arise again, thus requiring renewed repointing interventions. The paper describes a preliminary study conducted at Delft University of Technology to investigate the applicability of the innovative self-healing technology to enable an automatic repair of masonry cracks. A bacteria-based self-healing mortar, developed to repair existing concrete structures, was implemented to explore the capacity of couplets to recover their original strength and aesthetic aspect after multiple damaging events. Specimens built with calcium-silicate 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 strength restoration and aesthetic filling of cracks, occurs even after multiple cracking cycles when the self-healing mortar is used with both types of bricks, optimizing the autogenous healing of cement-based mortars. In this context, the healing effectiveness tended to decrease as the crack width and the number of cycles increased. 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 outcome provides the ground to delineate the remaining testing campaign.

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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.

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Sequentially Linear Analysis (SLA) is known for robust and reliable finite element simulations of masonry constructions, often considered challenging because of the brittle behaviour of the masonry material. Herein a sequence of scaled linear analyses is performed with decreasing secant stiffness of one integration point per analysis, representing local damage increments. This procedure is especially suited to simulate highly nonlinear collapse mechanisms. In this article, a benchmark experiment on structural historical masonry is first chosen. This benchmark is simulated using SLA, using the micro-modelling approach, with linear blocks/bricks and nonlinear interfaces using a multi-surface interface model. The results are compared against those of the experiment, nonlinear finite element analysis, and the Discrete Element Method (DEM), good agreement is found with those of the experiment, and the collapse mechanisms are also captured in a robust manner.@en

Due to the accompanying severe consequences of explosions, the blast puts a great threat to public security. Nonlinear finite element analysis is a possible method for civil engineers to check the integrity of the structures under blast loading without underestimating the limit of the structures. However, different choices of element types would generally put a great influence on the analytical results and the corresponding computational expenses. Therefore, how should civil engineers simplify their physical model into finite element models to gain relatively accurate numerical results with acceptable computational expenses is of great interest. In this article, 6 different types of elements are discussed with different orders and shapes for a certain physical situation, and the corresponding experimental results and the numerical results for a very detailed finite element model are used as the baseline for judgement, which could be helpful for civil engineers to make proper simplifications in the set-up of finite element models.

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Innovative solutions for seismic-retrofitting existing structures are currently required, as often traditional strategies are expensive, non-reversible, highly invasive, and/or fail to address both serviceability and ultimate limit states together. The present paper describes a preliminary experimental campaign performed at TU Delft to investigate an innovative structural glass window for strengthening masonry buildings. To this purpose, a prototype composed of a timber frame, a semi-rigid adhesive, and a 20 mm thick structural glazing layer was designed. The prototype aimed to improve the structure’s behavior against minor but more frequent service vibrations (SLS), as well as against ultimate ones (ULS). Specifically, an increase in the structure’s in-plane capacity and stiffness was targeted to reduce cracking at low drifts/displacements, while at larger drifts, the adhesive’s tearing and timber crushing were used to activate damping. To evaluate the prototype’s performance, a quasi-static, cyclic, in-plane test on a strengthened full-scale wall was performed and compared with available data on a similar, yet unstrengthened, wall. Although the benefits were not pronounced in terms of cracking and energy dissipation, the implementation of the proposed strategy provided an increase in terms of initial stiffness (18%), force capacity (8%, 36%), and ductility (220%, 135%). This outcome provides the ground for numerical studies that will help better delineate the proposed strategy and improve the current design.@en

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.@en

The city of Utrecht is famously known for the system of canals and the wharf cellars integrated to the heart of the city, whose construction dates back to the 1300s. Due to increased traffic volume which caused the increase in dead load and traffic load, it is important to assess the safety and state of maintenance of these historical structures. In this paper, a safety assessment framework for wharf cellars is introduced and the application to a wharf cellar as a case study in central Utrecht is provided. The geometry of the wharf cellar is parametrically generated and used for the numerical analysis using the distinct element method (DEM), where arch units and piers are modeled as discrete blocks separated by zero-thickness interfaces. Traffic load models in accordance with the Dutch guideline for emergency vehicles are calculated. Unlike traditional approaches, the three-dimensional load distribution through the soil is modeled. The structure’s compliance with this load is assessed, and the failure load and mechanism are observed. The analysis result can be used to help engineers on providing insights into the safety and stability of the cellars in an effort to extend the lifespan of the historical structures.@en

In the Netherlands, the potential damage to the building stock due to subsidence phenomena has recently received increased awareness. However, evaluating and predicting damage to buildings in subsiding areas is a complex task that requires associating the vulnerability of exposed structures with the intensity of the subsidence hazard. Considering the widespread presence of subsidence-related damage to the built heritage, the focus of this study is to provide empirical-based insights to assess and forecast subsidence damage to masonry buildings. A rich dataset with manual levelling measurements was collected comprising 386 surveyed masonry buildings, mainly low-rise (terraced) houses built before 1950. Of the total set of buildings, 122 cases rest on shallow foundations and 264 on piled foundations. For each building, the recorded damage is related to the settlement, calculated from the bed-joint levelling measurements, using four different intensity parameters, namely differential settlement, rotation, relative rotation and deflection ratio. These four parameters are appraised in their capacity to effectively predict the intensity of the damage. The Receiver Operating Characteristic (ROC) method is used to evaluate the relative efficacy of the selected hazard parameters. The rotation, the relative rotation (angular distortion) and the deflection ratio are observed as the most accurate when predicting the intensity of damage, while the differential settlement appears less accurate. Additionally, the dataset was used to generate empirical fragility curves where the probability of damage is described as a function of the aforementioned parameters. Thresholds were set to distinguish between the light damage and the functional and structural damage state. At a relative rotation of 1/500 masonry buildings on shallow foundations were observed to reach or exceed light damage with a probability of 13%, and functional and structural damage with 5%. The availability of the bed joint levelling measurements made it possible to classify eight recurrent settlement profiles, including both symmetric and asymmetric profiles, associated with both the overall deformation and the rigid rotations of the surveyed buildings.@en

Historical masonry façades are sensitive to various damaging processes. A recent study, looking at the initiation and progression of cracks in masonry, in the range of 0.1 to 5 mm in width and thus corresponding to light damage [1], has allowed for the calibration of finite-element models that include a material model capable of accurately replicating this damage and which is populated with material properties corresponding to existing structures [6]. The models, which also include a soil-structure interaction boundary designed to account for the effect of the soil during earthquake vibrations [7], have been used to determine the fragility of masonry buildings via the proxy of 2D walls [2]. In the study presented herein, the finite element models are employed to replicate the geometry of (historical) masonry facades to determine their sensitivity to light damage as a consequence of the two damaging processes observed to be most common for this type of façade, namely (differential) settlements and (earthquake) vibrations [3]. The masonry façades were first pre-damaged via settlement distortions which generate just-visible cracks in the order of 0.1 mm to 1 mm in width. Then, an acceleration time history corresponding to two different Dutch earthquake events and two recordings of traffic-induced building vibrations [9] were separately applied at the base of the models. In this manner, the effect of existing damage could be assessed in regards to the aggravation generated by vibrations. The settlement part of the study revealed that long façades were more vulnerable to applied soil distortions, for instance. Then, subsequent vibrations further increased damage for intensities measured with a peak ground velocity (PGV) larger than 2 mm/s while the control set of virgin or uncracked façades remained undamaged at this PGV. At 32 mm/s, many pre-damaged façades also exceeded the light damage range. At equal PGV, the traffic vibrations, with a larger number of effective cycles, resulted in increased damage aggravation in comparison to the earthquake recordings.

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The shove test (ASTM Standard C1531) is an experimental technique aimed at studying the shear-sliding behavior of brick masonry. It can be executed according to various testing methods that differ in the way the vertical compression load is applied and in the way bricks and/or joints are locally removed for inserting jacks. One of the most critical aspects is the correct evaluation of the compressive stress state on the sliding brick. The objective of the present paper is to investigate the capability of the shove test in determining the shear strength parameters of brick masonries and to highlight the main advantages and disadvantages of the various testing methods. To this aim, nonlinear numerical simulations of the shove test were performed by adopting a brick-to-brick modeling strategy. The 2D numerical model was calibrated and validated through comparisons with experimental results of triplet tests and shove tests. The numerical analyses allowed to understand the influence the different testing methods and the masonry mechanical properties, such as dilatancy, may have on the test results. Based on the numerical outcomes, correction factors were calibrated for the proper evaluation of the compressive stress state on the sliding brick. Improvements with regards to the experimental procedures, i.e. additional test phases and measurements, were also proposed to enhance the results interpretation.

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Perforated unreinforced masonry (URM) walls in out-of-plane (OOP) two-way bending are commonly encountered in natural hazard investigations. However, related research is rather limited. This study focuses on the influence of openings on the two-way bending capacity of URM walls. An experimental database about the perforated URM walls in OOP two-way bending was created. A brief review of the experimental results show that the arrangement of the opening area can significantly affect the two-way bending capacity of walls (defined as the peak pressure on the wall net area): when the opening area is non-covered and non-loaded, the two-way bending capacity of the perforated wall is higher than that of its solid counterpart; when the opening area is covered with timber or glass plates loaded as the rest of the wall, the two-way bending capacity of the perforated wall is lower than that of the corresponding solid wall. These observations from the experiments were confirmed by an analytical estimation using the Yield Line Method (YLM). Next, to study the influence of openings on the two-way bending capacity, a numerical study has been carried out by employing the 3D simplified brick-to-brick modelling approach. The results of calibration and validation show that this modelling approach can precisely predict the two-way bending capacity and crack patterns. By applying the validated numerical models, the influence of the arrangement for the opening area from the experimental results and YLM evaluation was confirmed. Further, a parametric study focusing mainly on cases with the opening area non-covered and non-loaded was conducted. The influence of the geometric parameters of openings, namely, the opening size, shape and position was investigated on walls with different aspect ratios. Results show that the two-way bending capacity increases as the opening size or aspect ratio (height to width) increase, but it is insensitive to the opening position. Eventually, based on the numerical results, analytical equations were proposed to account for the influence of the considered parameters on the two-way bending capacity. A comparison with the Australian Standard (AS3700) indicates that the proposed equations incorporate more opening parameters such as opening shape.

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