Low-rise masonry buildings worldwide frequently feature unreinforced masonry (URM) walls coupled with various pitched roof configurations supported by masonry gables. Past earthquakes have highlighted the vulnerability of these components to out-of-plane seismic loads due to their high slenderness, insufficient roof connections, and exposure to amplified accelerations while being subjected to minimal overburden due to their location at the upper part of buildings. This study presents key insights from the experimental campaign of the ERIES-SUPREME project, aimed at enhancing the understanding of the out-of-plane seismic behavior of masonry gables. Incremental dynamic tests were performed on three full-scale URM gables, simulating both induced and tectonic earthquake scenarios until collapse, using two shake tables. Differential motions at the top and bottom tables reproduced the interaction of the gables with three different roof diaphragm configurations, each introducing a unique filtering effect on the seismic input. The outcomes of the experiments can be used for refining existing numerical modelling strategies as well as contribute to developing improved tools for the seismic assessment of URM gables.

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.

Masonry quay walls are vital infrastructure in many historic cities, serving both functional and historical purposes. Originally designed as gravity retaining walls, they now face increased vehicle loads and widespread material degradation, particularly in timber foundations. Traditional assessment methods are often overly conservative, lacking standard procedures for multi-wythe masonry characterisation.With over 200 km of quay walls in Amsterdamrequiring renovation, there is an urgent need for practical, reliable assessment methods. This paper provides an overview of recent research conducted at TU Delft with focus on the response of masonry superstructure, presenting and discussing key advancements in the development of high-fidelity static and dynamic finite element models and minor-destructive testing for masonry mechanical property characterisation.

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.

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.

Damage and collapse of walls in the out-of-plane (OOP) direction are common failure modes in existing unreinforced masonry (URM) buildings when subjected to seismic excitation. These localized mechanisms also hinder the realisation of the complete in-plane seismic capacity of URM buildings. Among such OOP failures, a distinction can be made between (i) one-way bending which occurs in long walls and walls without side supports, and (ii) two-way bending which occurs in walls that have at least one vertical and one horizontal edge supported. This paper examines the suitability of a single-degree-of-freedom model for modelling the dynamic behaviour of URM walls subjected to OOP seismic excitation and undergoing two-way bending. The model operates in two phases: (i) initial elastic and (ii) post cracking, transitioning instantaneously between the phases once the force required to crack the wall is surpassed. Post cracking, the wall is treated as a system comprised of rigid blocks, and wall resistance is computed by combining three distinct contributions. These contributions are (i) bilinear elastic rigid block rocking, (ii) elastoplastic friction, and (iii) bilinear degrading component taking into account strength and stiffness degradation of walls. The model's complete behaviour in both phases is described by six independent parameters, which can be computed analytically. This paper explores the performance of the proposed model, especially when compared with and calibrated against experimental results from incremental dynamic testing of full-scale single leaf and cavity walls, for which the model demonstrates excellent agreement.

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 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.

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.

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.

Historical quay walls, constructed in unreinforced masonry, play a crucial role in the infrastructure of many Dutch cities. Designed originally as gravity retaining walls, these structures are increasingly subjected to traffic loads due to vehicles operating on roads built on their backfill. This study conducts a preliminary numerical evaluation of a strengthening technique aimed at prolonging the service life of such quay walls, focusing on a specific case in Amsterdam. The strengthening method involves drilling tubular steel piles through the existing masonry to anchor into a stable soil layer, with the piles bonded to the masonry using low-shrinkage casting concrete. The assessment models the interaction between the strengthening technique and the existing quay structures, including a detailed simulation of the installation process, identified as critical for proper simulation of the structural behaviour. While the technique significantly enhances the quay's force capacity, an improvement in displacement capacity was not evident, highlighting the need for further investigation.

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.

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.

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.

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 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.

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.

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.

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.