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.

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.

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.

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.

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.

The assessment of the seismic performance of unreinforced masonry cross-vaults is still a challenge in numerical analysis, due to complex curved geometries and bond patterns, and uncertainties related to the selection of adequate modeling strategies, including but not limited to that of material properties, damping scheme, and unit/joint idealization. This paper presents the results of a collaborative effort to validate, against the shake table test of both unstrengthened and strengthened masonry cross-vault specimens as part of the SERA Project Blind Prediction and Post-diction Competition, various discontinuum-based numerical approaches. First, the geometry of the cross-vault is created using a Python-based computational framework to accurately represent the brick arrangement and the shape of the vault. Then, the geometry is converted into an assemblage of deformable blocks and analyzed using the Distinct Element Method (DEM). An elasto-softening contact model based on fracture energy is implemented in the masonry joints to simulate crushing, tensile, and shear failures. The performance of the proposed strategy, conceived for the unstrengthened configuration of the tested vault specimen and then adapted to include the presence of cementitious repairs, shows satisfactory agreement with both qualitative and quantitative experimental responses, also revealing critical insights and lessons learned through the blind/post-prediction exercise.

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.