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 investigates settlement-induced damages in unreinforced masonry (URM) walls using a high-fidelity block-based numerical modeling approach. The research aims to address gaps in the understanding of settlement effects on URM walls with flanges, particularly with respect to their seismic out-of-plane (OOP) behavior. A parametric study is conducted on four wall specimens with varying geometries, boundary conditions, and settlement scenarios, including symmetric and asymmetric patterns. The numerical models are developed via a high-fidelity block-based finite element method that simulates masonry using expanded blocks connected by zero-thickness joints, allowing for detailed analysis of cracking patterns and damage mechanisms. Different damage states, from no visible cracks to near-collapse conditions, are identified in the response of the walls and are used as initial conditions for subsequent monotonic static pushover OOP loading. The results highlight the significant influence of settlement-induced pre-damages on the OOP response of URM walls, with varying degrees of impact observed across different specimen configurations. The findings underscore the importance of considering even “light” settlement-induced pre-damages when assessing the seismic performance of URM structures, particularly in subsidence-prone regions. Under symmetric hogging, such pre-damage level can reduce OOP stiffness and peak strength by up to 41% and 20%, respectively. This study lays the groundwork for future investigations into the seismic behavior of pre-damaged masonry structures under dynamic loading and offers valuable insights for the development of more accurate assessment and mitigation strategies for buildings subjected to settlement deformations.

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 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.

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 study presents a numerical investigation into the effects of salt crystallisation-induced weathering on masonry earth-retaining walls, with a specific focus on historic quay walls in Amsterdam. A multiphase modelling strategy is adopted to simulate moisture and salt transport, capturing the impact of environmental exposure on these ageing structures. The numerical model is first applied with masonry assumed as a homogeneous continuum and is subsequently refined to incorporate masonry texture. The influence of boundary conditions, multiple weathering cycles, and long-term humidity variations is examined to assess salt accumulation patterns. Results indicate that evaporation pathways significantly influence crystallisation depth, while explicitly modelling masonry texture leads to greater salt accumulation. Furthermore, an analytical estimation of the effective Young's modulus suggests that salt deposition within pores may contribute to through-thickness stiffness variations observed in experimental studies on samples collected from a multi-wythe masonry bridge pillar, with masonry type and exposure conditions comparable to those of Amsterdam's quay walls. These findings provide new insights into the deterioration mechanisms of historic quay walls and highlight the importance of considering environmental effects in their structural assessment.

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.

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.

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.

Typical low-rise masonry buildings worldwide often feature unreinforced masonry (URM) walls paired with pitched roof configurations supported by masonry gables. Past earthquakes indicate that these components are vulnerable to out-of-plane seismic loads. This study presents key findings from the experimental campaign of the ERIES SUPREME project, which aims to advance understanding of the out-of-plane seismic response of masonry gables. Incremental dynamic tests simulating induced and tectonic seismicity scenarios were conducted on three full-scale URM gables, using two shake tables. Differential motions applied to the top and bottom tables allowed the simulation of gable interaction with distinctly different roof configurations. The experimental results are presented in terms of failure mechanisms, force-displacement hysteresis behavior, and acceleration and displacement capacities. These findings will contribute to refining and calibrating existing numerical models.

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.

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.

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.

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.

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.

Environmental factors, projected to intensify due to climate change predictions, can expedite the degradation and aging of historic building materials like masonry. Among the primary degradation risks, salt crystallization stands out. Historical masonry quay walls, a vital component of the infrastructure of numerous European cities, notably in the Netherlands, present a unique case study in this aspect. This uniqueness arises from their continuous and long-term exposure, not only to environmental influences but also to salts in the canal water. To investigate this, a coupled multiphase modeling strategy for the hygrothermal analysis of masonry structures is used to simulate the impact of salt crystallization on multi-wythe masonry quay walls in the city of Amsterdam. This modeling strategy is governed by four highly nonlinear and fully coupled differential equations addressing moisture mass conservation, salt mass conservation, energy balance, and salt crystallization/dissolution kinetics. The model has been previously validated against laboratory experiments, but it is here applied for the first time to a real case study. A parametric study adopting a 2D sectional numerical model of the quay wall was performed. Parameters investigated include the effects of boundary conditions at different faces of the quay wall, masonry bond pattern, salt concentration in the water as well as time variance of environmental relative humidity. The findings of this paper can be used to identify critical environmental conditions for quay walls as well as provide the basis for explaining the through-thickness variation of mechanical properties found in previous research.

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.

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.

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.