Simulating the seismic behaviour of unreinforced masonry (URM) is challenging due to large deformations and severe damage. Capturing this highly nonlinear response requires advanced numerical modelling strategies that represent block separation, debonding, friction, and impact. Discontinuum-based modelling strategies, such as the Distinct Element Method (DEM), are well suited, as they explicitly represent bond failure and damage progression from cracking to collapse. DEM relies on the explicit time integration scheme of motion equations; hence, the choice of the damping scheme becomes critical. Typically, mass-proportional damping is used in dynamic analysis, often without complementing it with stiffness-proportional damping which requires unpractical reduction of the time steps to ensure numerical stability. Yet relying solely on mass-proportional damping can overdamp low frequencies and underdamp high frequencies. This study implements and validates an alternative damping approach, Maxwell damping, where multiple spring-dashpot elements are introduced at unit-mortar interfaces within a simplified micro-model. This work introduces an optimization algorithm to tune the Maxwell elements without heuristics, targeting near-uniform damping over a broad frequency range. Effectiveness is assessed against shake-table tests on a full-scale cross-vault URM specimen. Predicted displacements, accelerations, damage evolution, and computational efficiency is compared with mass-proportional and zero-viscous damping models. This study investigates Maxwell damping as a practical relaxation scheme for the seismic analysis of complex masonry systems using DEM, building on prior formulations in the literature and extending them to the present modelling and validation context.

An existing interface material model for quasi-brittle fracture, originally developed within the Discrete Element Method framework, is implemented and enhanced for use in implicit Finite Element analyses of unreinforced masonry structures. The model captures mixed-mode fracture in tension-shear and combines cohesion with Coulomb friction in compression-shear. To address convergence issues arising when loading–unloading takes place, due to a discontinuity in the traction–separation relation, a regularization of the frictional contribution is proposed. A new model parameter is introduced and a calibration procedure to ensure numerical robustness and objectivity is presented. Furthermore, the consistent tangent stiffness matrix is derived to improve convergence in full-scale simulations. The improved model is applied within a simplified micromodelling approach to simulate the in-plane cyclic response of 2D masonry structures, including a shear wall and a spandrel subjected to a combination of horizontal and vertical actions. The results demonstrate that the model accurately reproduces key aspects of masonry behaviour, including stiffness degradation, energy dissipation, and crack patterns, while maintaining robustness and efficiency in complex cyclic loading scenarios.

Growing incidents of structural damage and failures underscore the urgent need for more advanced Structural Health Monitoring (SHM) solutions. While Multi-Temporal Interferometric Synthetic Aperture Radar (MT-InSAR) has revolutionised SHM by enabling automated, long-term, and large-scale displacement monitoring of structures using Persistent Scatterers (PSs), its applicability is often constrained by the unpredictable spatial distribution of PSs. Conventional suitability assessments that rely primarily on PS density fail to account for the underlying structural behaviours, limiting their reliability.

This paper introduces a novel structural-based inverse approach that uniquely integrates MT-InSAR characteristics with structural response modelling to overcome these limitations. Unlike existing approaches, the method explicitly evaluates whether observed surface displacements adequately represent a target damage mechanism by comparing outputs from a pseudo sensor with those from a virtual MT-InSAR sensor. If this condition is satisfied, it then determines the minimum required number and optimal spatial arrangement of ideal PSs using modified pivoted QR factorisation, where satellite-induced positional uncertainties are rigorously modelled through Radial Basis Function kernels.

The proposed method was validated on a quay wall in Amsterdam using Finite Element Method (FEM) simulations of three distinct damage mechanisms. Results demonstrate its unique capability to quantitatively assess displacement representativeness and to pinpoint ideal PSs for robust monitoring. Leveraging these insights, the method was further applied to evaluate MT-InSAR monitoring feasibility across Amsterdam’s historic centre, successfully identifying quay wall segments amenable to reliable observation. This work represents a significant advancement in MT-InSAR-based SHM, providing a more targeted and structurally informed approach for real-world infrastructure monitoring.

This paper presents a cyclic joint constitutive model within a Distinct Element Method framework to simulate the in-plane response of unreinforced masonry structures. The model combines multi-surface failure criteria, including tensile cut-off, Coulomb friction, and an elliptical compression cap. It incorporates exponential softening, a unified damage scalar for stiffness degradation, and a hardening–softening law for compression. Shear-induced dilatancy is captured via an uplift-correction mechanism with an exponential dilatancy-decay law, while stiffness degradation governs energy dissipation. The model is validated at both material and structural scales. Material-level simulations of cyclic compression and shear tests show close agreement with experimental data. Structural-scale validation on full-height calcium-silicate walls under combined compression and cyclic lateral loading demonstrates the ability to reproduce rocking-dominated, shear-dominated, and hybrid failure mechanisms. The model successfully replicated global hysteretic force–drift loops, capturing stiffness decay and energy dissipation, as well as local failures like cracking, sliding, and toe crushing. The model also reproduced the drift-dependent transition from rocking to friction-controlled sliding, a key mechanism for earthquake assessment. By integrating these features into a single, efficient framework, the proposed constitutive model provides a robust tool for evaluating seismic performance and conserving heritage.

This paper presents a comprehensive review of the effects of interactions between in-plane (IP) and out-of-plane (OOP) behaviors, referred to as IP-OOP interactions, on the seismic behavior of framed unreinforced masonry structures, consolidating findings from experimental, numerical, and analytical studies available in the literature. While masonry structures are highly vulnerable to seismic loading and undergo multi-directional seismic actions, most existing research focuses on their response to unidirectional forces, overlooking the complex interaction effects observed during real earthquakes. Moreover, although design and assessment standards acknowledge these interactions, they offer limited prescriptive guidance. The literature predominantly addresses the impact of IP pre-damage on OOP strength and stability (IP/OOP interaction), with comparatively fewer studies examining the reverse scenario, i.e., OOP pre-loading affecting IP resistance (OOP/IP interaction). Experimental data remains scarce, particularly for multi-bay frames and walls with openings, limiting the generalizability of current findings. Numerical simulations have significantly advanced the understanding of these interactions, yet their reliability relies on proper calibration against benchmark experiments, which are still limited in number. Among the most influential parameters affecting the effect of IP pre-damage on the OOP response, the height-to-thickness slenderness ratio plays a dominant role. Slender walls are especially prone to severe OOP strength degradation due to reduced arching action and increased instability. The length-to-height aspect ratio also influences failure modes under IP/OOP interaction, particularly in short walls where horizontal arching action reduces. Other critical factors, such as masonry material properties, boundary conditions, and frame stiffness, have been identified, but their effects remain less systematically studied. Analytical approaches have primarily focused on IP/OOP interaction effects. However, existing equations are often derived from limited datasets, restricting their predictive capabilities. The equation widely adopted in seismic guidelines has been shown to overestimate OOP strength reduction, underscoring the need for more refined models that incorporate broader experimental and numerical data. Future research should address these gaps by expanding experimental campaigns, enhancing numerical methodologies, and refining analytical frameworks to better represent real-world conditions.

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 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.

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.

Unreinforced masonry gables are widely present in low-rise existing buildings and are particularly vulnerable to seismic events, as demonstrated by the several observed out-of-plane collapses of these structural elements during earthquakes. Since the structural behaviour of gable walls has been scarcely investigated in the literature, a large-scale testing programme (ERIES-SUPREME) has been initiated by research institutions in the Netherlands (TU Delft, TNO) and Italy (EUCENTRE, University of Pavia, IUSS Pavia), to dynamically characterise the gable out-of-plane seismic response. Shake-table tests on full-scale masonry gables are being conducted at the 9D LAB facility in EUCENTRE (Pavia, Italy), incorporating the effects of different ground motions, structures and roof stiffnesses. This facility features both a top and a bottom shake table, allowing for separate input motions: therefore, the effect of the roof dynamic behaviour can be accounted for by applying differential signals. This work presents the procedure used to define such input motions. While for tectonic signals direct earthquake recordings at floor level are accessible from existing monitored masonry buildings in Italy, for induced signals in the Netherlands such data are not available. Thus, in the latter case, numerical analyses are conducted considering a reference unreinforced masonry building subjected to induced earthquakes, with three roof configurations representing flexible, semi-flexible, and stiff diaphragms. Based on the obtained outcomes, input signals are derived for both induced and tectonic earthquake scenarios, leading to the final definition of the testing protocol for the ERIES-SUPREME experimental campaign. The findings of this study are also broadly applicable for the derivation of input motions in the planning of benchmark experiments where parts of the structural system cannot be explicitly reproduced due to testing constraints.

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 article presents a dataset from an experimental campaign investigating the out-of-plane (OOP) seismic response of unreinforced masonry (URM) gables in existing buildings. Addressing a critical gap in published research, the dataset provides novel experimental data on the incremental dynamic OOP behavior of three URM gables tested under seismic loading until full collapse. All three gables were nominally identical but differed in their interaction with the supporting roof structure. This interaction was experimentally reproduced by imposing differential motions at the top of the gables, which were either linearly amplified or both amplified and phase-shifted relative to the motion at the base. This approach ensured idealized and numerically replicable boundary conditions, making the dataset an ideal benchmark for refining existing and developing new modeling approaches for URM structures. The dataset includes measured and calculated acceleration, displacement, and force time histories. Beyond supporting the validation and development of numerical models, it can also contribute to improving guidelines for the out-of-plane seismic assessment of URM gables and is openly available for further research and engineering applications.

Typical low-rise masonry buildings worldwide commonly feature unreinforced masonry (URM) walls, often paired with various pitched roof configurations supported or finished by masonry gables. These buildings constitute a significant portion of the building stock in several seismic-prone regions, including areas vulnerable to both natural and induced seismicity. Masonry gables in such buildings are frequently associated with high seismic vulnerability, as evidenced by damage observed after past earthquakes. This paper presents key results from an experimental campaign aimed at enhancing the understanding of the seismic out-of-plane response of masonry gables. Incremental full-scale shake-table tests were performed on three densely instrumented URM gables until the complete collapse. Within this context, the study systematically investigated the effects of motions applied at the top of the gable, both being linearly amplified as well as amplified and out-of-phase, with respect to the motion applied at the base of the gable. Such differential motions simulate the effect of the gable interaction with three different roof configurations, each exerting a different filtering effect on the seismic motion. The response of the gables to both induced and tectonic earthquakes was considered. The experimental findings are presented in terms of failure mechanisms, force-displacement hysteresis behaviour, and acceleration and displacement capacities. All generated experimental data, along with the associated instrumentation schemes, are openly available for download at https://doi.org/10.60756/euc-1avy7q49.

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.

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.

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.

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.

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 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.

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 collapse of walls in the out-of-plane (OOP) direction is a common failure mechanism in existing unreinforced masonry (URM) buildings when subjected to seismic excitation. Such local mechanisms also prevent the realisation of the full in-plane seismic capacity of URM buildings. Among OOP failures, a distinction can be made between (i) one-way bending which occurs 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 proposes 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 considers two distinct phases: (i) initial elastic and (ii) post cracking, transitioning instantaneously between the two once the force required to crack the wall has been exceeded. The model's complete behaviour (i.e. in both phases) is described by six independent parameters, which can be calculated analytically. Post cracking, the wall is treated as a system composed of rigid blocks, and the wall resistance is calculated as the superimposition of three separate contributions: (i) the bilinear elastic rigid block rocking, (ii) the elastoplastic friction, and (iii) a bilinear degrading component taking into account strength and stiffness degradation of the wall. The proposed model is then calibrated against experimental results from incremental dynamic testing of full-scale walls. For this, two walls with different failure modes under horizontal bending, i.e. line and stepped failure are considered. Calibration of the model shows excellent agreement with test results, successfully capturing their behaviour from cracking to collapse. The calibrated models were employed to evaluate behaviour factors under both natural and induced seismicity, resulting in values close to two for both walls.