This paper introduces novel analysis procedures for the structural assessment of masonry earth retaining structures subjected to traffic loading. Given their substantial presence, particularly in transportation networks of historical cities, and the challenges posed by ageing, deterioration, and exposure to loads beyond their original design considerations, this research highlights the necessity of accounting for potential load redistribution mechanisms during their assessment. This can prevent overly conservative interventions that may not be necessary and also contravene sustainability and heritage preservation principles. Four distinct analysis procedures – 2D monotonic, 3D monotonic, 3D static moving load and 3D dynamic moving load – are developed, each progressively more refined than its predecessor in capturing potential load redistribution mechanisms in masonry earth retaining structures. These mechanisms may develop due to the dynamic loading conditions of the vehicular passage, the 3D structural configuration of retaining structures, and non-linear material behaviour. By comparing the structural capacity evaluated using the four procedures, contributions from different sources of load redistribution can be separately quantified, aiding in the reduction of conservatism inherent in less refined assessment procedures. The application of the developed procedures and consequent quantification of load redistribution is demonstrated through a case study of an existing masonry retaining structure in Amsterdam, the Netherlands.

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The implementation of effective and sustainable Structural Health Monitoring (SHM) systems for the evaluation of infrastructure conditions is critical to address the deterioration and damage experienced by structures worldwide. Given the vast number of structures involved, resorting to traditional in-situ visual inspections and data gathering methods is becoming increasingly unfeasible. Multi-Temporal Interferometric Synthetic Aperture Radar (MT-InSAR) has recently gained attention as a viable solution for long-term SHM. This remote sensing technique combines multiple satellite radar images to measure changes in the Earth’s surface over time. Unlike conventional techniques, MT-InSAR does not require in-situ installations and offers extensive coverage, enabling observations across diverse location and structures. However, the applicability of MT-InSAR monitoring depends on the relatively unpredictable distribution and location of permanent scatterers (PSs), which are influenced by surface characteristics and vegetation changes. Evaluating the reliability and capacity of MT-InSAR is therefore crucial to enhance its effectiveness in assessing the location and extent of structural damage. In this study, we present an effective approach to determine the optimal number and position of PSs for detecting different structural damage mechanisms. The approach is exemplified through a case study of a quay wall in Amsterdam, with data inputs simulated using the Finite Element Method. The proposed method has the potential to evaluate the feasibility of MT-InSAR for a broader range of scenarios, enabling to detect specific structural conditions.@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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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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Unreinforced masonry buildings show high vulnerability to seismic loading, especially in the out-of-plane direction. Two-way spanning walls are characterized by effective restraints at at least one lateral side of the wall. Their seismic performance under out-of-plane loading has been studied in the literature for walls without openings or with one opening, but it lacks understanding in case of multiple openings. This study presents an engineering approach to calculate the out-of-plane capacity of two-way spanning walls with two openings. Five wall configurations were analysed via non-linear pushover analyses, and crack-pattern evolution tracked. A methodology was proposed which involves dividing the wall into panels whose performance is assessed separately. The division is based on the crack propagation observed in the numerical simulations. Two panels are defined as the wall portions comprised between a side support and an opening which are classified and analysed as three-sided supported walls. Another component corresponds to the wall portion between the two openings and is analysed as a one-way spanning wall. The assessment of the individual panels is based on formulations provided in the Dutch guidelines NPR-9998:2020 which show that the one-way spanning wall panel is the governing one, which is further proved by the analytical calculations.

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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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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

Canals delimited by masonry quay walls are integral elements of many cities in the Netherlands. Historically built to enable the efficient transportation of goods, today such infrastructure also gives the cities their historical and monumental character. In recent years, many quay walls in the Netherlands have shown substantial deformation and damage, and in few cases even collapse. Historical quay walls, which are constructed in thick multi-wythe unreinforced brick masonry and are supported on a system of timber piles, nowadays sustain traffic loads larger than the one they were designed for. Instances of collapse and severe damage has given rise to a need for research assessing the safety of these structures, which are not appropriately covered by any normative or standardised guidelines. This paper presents a novel methodology to numerically assess the performance of masonry walls in historical quays under the dynamic effect of traffic loads. Application of the proposed methodology to a case study in Amsterdam, the Netherlands, is presented.@en

Historical quay walls constructed in unreinforced masonry are integral elements of many cities. Originally designed as gravity retaining walls, they are nowadays often subjected to the action of traffic loads as a result of vehicles travelling on roads constructed on their backfill. This paper presents a numerical analysis procedure for carrying out the structural assessment of quay walls under traffic loads. The procedure simulates the non-linear dynamic response of the quay wall under the effect of the passage of a vehicle. Non-linear dynamic calculations are performed not only to be representative of the actual nature of loading but also to produce realistic estimations of structural safety, load redistribution capacities and displacements. Adopting a tier-based approach, the computational burden typically associated with such simulations is significantly reduced. This is obtained by adopting simplifications which allow for the modelling the 3D soil block comprising the backfill of the quay wall only in the first tier of the procedure. To demonstrate the implementation of the procedure, a detailed application to an existing quay wall in Amsterdam, the Netherlands, is presented. Different foundation damage scenarios are also considered. Though the procedure is presented in this paper for a specific typology of quay walls, it has conceptual and methodological value. With appropriate modifications it can be used for the structural assessment of other earth retaining structures as well, under the effect of vehicular traffic on their backfills.@en

This paper presents the results of an experimental campaign carried out to characterise the mechanical properties of multi-wythe masonry infrastructure in the city of Amsterdam. Samples were extracted from a 1.2 m thick bridge’s pillar constructed in 1882. For the characterisation of shear and compressive properties of masonry, tests on cores with a 100 mm diameter were performed at the Stevinlaboratorium of Delft University of Technology. Samples were extracted along different locations in the wall thickness to evaluate the effect of exposure to environment conditions. Overall, the study provides a first insight on the mechanical properties of multi-wythe masonry city infrastructure and knowledge regarding the sampling and testing strategy for these structures. In turn, this will increase the knowledge on multi-wythe masonry, which is limited in literature, and will support the assessment of many infrastructures in typical Dutch canal cities.

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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

Plane-stress and shell macromodels are often preferred to analyze masonry structures because of their numerical efficiency. However, they often misestimate the hysteretic behavior of the structures. Additionally, due to the nature of smeared cracks, the cracks may be diffused. This article proposes a new orthotropic model, which focuses on the cyclic, nonlinear behavior of brick masonry structures. The model adopts a total-strain based rotating crack approach. It describes tensile and compressive failure in the rotating principal directions, while including indirectly shear failure through an internal iterative algorithm. Two distinctions are made regarding the tensile postpeak and unloading/reloading behavior based on the crack orientation at crack initiation: a steep softening branch and secant unloading are adopted when the crack angle corresponds to in-plane flexural failure, and a softening branch and bilinear unloading are adopted when the crack angle corresponds to diagonal shear failure. Bilinear unloading/reloading is adopted in compression, resulting in a cyclic behavior resembling shear. The constitutive model was implemented in a finite element software and validated against experimental results. The numerical simulations reproduced well the experimental outcomes in terms of envelope load-displacement curve and hysteretic behavior, while simultaneously they resulted in localized damage, representative of the experimental crack patterns.

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Since the 1980s, calcium silicate element masonry has been commonly used in Dutch buildings, and vertical continuous joints have been usually located at the corner of perpendicular walls. Since the shear failure of these joints may significantly reduce the seismic performance of the flanged wall and therefore of the entire building, the assumption of rigid connection may be inaccurate, unlike for the traditional interlocking of bricks in running bond textures. In this paper, analytical and numerical approaches to study the failure of vertical joints in the seismic assessment of URM buildings are presented. The first part of the work focuses on two different numerical models to study the nonlinear behaviour of the vertical connection; the related critical numerical issues are then discussed. The second part introduces an analytical method able to estimate the lateral force–displacement curve of a flanged wall, which considers the possible failure of the connection. In particular, the method is derived from the section analysis approach developed for controlled rocking deformable systems. The comparison between the numerical simulations and the analytical method proves the capacity of the latter to provide a quick but sufficiently accurate estimate of the force–displacement curve of a URM U-Shaped wall.

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In the province of Groningen (NL), where human-induced earthquakes take place due to gas extraction, a large part of the building stock is composed of brick masonry walls and timber diaphragms. In this framework, timber-masonry connections play a crucial role in the global seismic response of the buildings, but their properties and structural behaviour have not been investigated yet for the Dutch context. This work describes the experimental campaign conducted at Delft University of Technology to characterize as-built and strengthened timber-masonry connections. The joints were tested under either quasi-static monotonic, cyclic or dynamic loading, to analyse the effect of an induced earthquake signal on the connections’ response in terms of strength, stiffness and damage evolution. The obtained test results provided more insight into the capacity and properties of existing connections, and useful knowledge on the effectiveness of the tested retrofitting methods.

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Terraced houses built in the Netherland after 1980 are often characterized by the use of large units connected at corners by continuous thin layer mortar joints. Unlike the running bond pattern, usually modelled as a rigid connection, the vertical continuous connection may fail in shear and influence the global seismic capacity of the entire building. This work aims at investigating and comparing different numerical modelling approaches for simulating the vertical connections. Two different constitutive models are adopted to simulate the quasi-brittle nonlinear behaviour of the continuous joint, and their advantages and limitations are pointed out in terms of robustness and accuracy. The study considers both the component level in terms of U-shaped pier-wall configuration, and the full-scale structural level in terms of the global capacity for a two-storey masonry house assemblage, characterized by a running bond arrangement. The results of this work show that the shear failure involving the continuous joint usually reduces the strength capacity of the structure. Both the selection of constitutive models for the connection interface and masonry material are demonstrated to affect the results significantly. Decoupled direct traction-displacement relations for the interfaces appear to provide more robust results than coupled plasticity-based Coulomb friction laws. The selection of either a pre-fixed orthotropic smeared crack model for the masonry or a standard isotropic concrete-like rotating smeared crack formulation is demonstrated to strongly influence the activation of the different failure mechanisms and hence the response of the structure.

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In recent years, the number of human-induced earthquakes in Groningen, a large gas field in the north of the Netherlands, has increased. The majority of the buildings are built by using unreinforced masonry (URM), most of which consists of cavity (i.e. two-leaf) walls, and were not designed to withstand earthquakes. Efforts to define, test and standardize the metal ties, which do play an important role, are valuable also from the wider construction industry point of view. The presented study exhibits findings on the behavior of the metal tie connections between the masonry leaves often used in Dutch construction practice, but also elsewhere around the world. An experimental campaign has been carried out at Delft University of Technology to provide a complete characterization of the axial behavior of traditional connections in cavity walls. A large number of variations was considered in this research: two embedment lengths, four pre-compression levels, two different tie geometries, and five different testing protocols, including monotonic and cyclic loading. The experimental results showed that the capacity of the connection was strongly influenced by the embedment length and the geometry of the tie, whereas the applied pre-compression and the loading rate did not have a significant influence.

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In the last two decades, the province of Groningen, located in the North-East of the Netherlands, has been subjected to an increasing number of earthquakes induced by gas extractions. The existing building stock is mainly composed by unreinforced masonry (URM) buildings not conceived to resist seismic loads. The need of reducing the vulnerability of these buildings by means of retrofit interventions, led to the development and adoption of a new guideline (NPR9998:2018). As regards the seismic assessment of URM buildings using nonlinear static analysis, the guideline includes significant differences with respect to Eurocode 8, which is adopted in other European countries. The more significant differences lay in the description of failure mechanisms and constitutive laws of piers and spandrels, in the identification of limit states and in the calculation of seismic demand. In the last years, the assessment and retrofit in the region has been carried out using software based on an equivalent-frame strategy: among these, the 3Muri software has been widely adopted. The solver of this program is the research software TREMURI. In this work, a new version of the solver adopted by the software 3Muri, complying with the requirements of the new Dutch guideline, was developed; the tool was then validated with simple examples. To illustrate the specificities of the new guideline, the seismic assessment of a building representative of one of the most widely diffused URM building typologies in the area was performed.@en

This paper proposes a sub-step based iterative constitutive model for line interface elements used to analyse masonry structures loaded in-plane. Based on a total deformation theory, the model adopts characteristics of multi-surface plasticity, including a Coulomb friction failure surface for shear, with tension and compression cut-off and softening for all three domains. The model is driven by two damage parameters, one for compression and one that couples tension and shear. The sub-stepping technique is demonstrated to be numerically stable and is used as an alternative to the traditional return-mapping algorithms, which are prone to convergence issues and instability. The proposed model has been validated against experimental tests performed on masonry walls subjected to cyclic, in-plane loading. The numerical simulations adequately identify the failure mode, the hysteretic behaviour and the crack pattern. When toe crushing is governing, the results appear to be sensitive to the assumed masonry compressive strength. It is shown that calibration of the lumped compressive strength makes possible to fully describe the damage evolution in walls that exhibit a mix of flexural crack-crush failure and shear failure. Overall, the model is demonstrated to be an efficient and robust tool for analysing the cyclic, in-plane behaviour of masonry walls.

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In recent years, the seismic risk in the north of the Netherlands has increased due to gas extraction. Since 2014, the Delft University of Technology started a research program to assess the seismic response of unreinforced masonry (URM) buildings. The Dutch URM buildings are characterized by slender piers and transverse walls. In common practice, the connections between piers and transverse walls are often modelled as rigid, but in real structures these connections may exhibit different behaviour. Especially, since the 1980s, calcium silicate element masonry has been commonly used in Dutch buildings, and vertical continuous joints are present between transverse walls. For this reason, it appears essential to assess the connection strength properties, since its failure can significantly reduce the seismic performance of the entire structure. The first part of this work investigates and compares different numerical approaches to describe the nonlinear behaviour of masonry under lateral loads, simulating seismic action. The second part specifically focuses on the critical issues related to the modelling of vertical connections of Dutch URM buildings. A sensitivity study of the frictional parameters is performed to analyze the influence of the strength of the glued connection on the global response of the URM structure.@en