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J.G. Rots
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This study investigates the effects of differential support motions, caused by filtering effects due to the building response to earthquakes, on the one-way bending out-of-plane (OOP) behavior of unreinforced brick masonry walls, a factor often overlooked in seismic assessments. A high-fidelity block-based numerical model is used to simulate walls with varying slenderness ratios, precompression levels, and boundary conditions. Floor motions from shake-table tests on two-story masonry buildings with flexible and rigid attic diaphragms under induced and tectonic seismicity are applied at the top and base boundaries of the models as loading signals. Results show that differential motions between supports significantly influence OOP wall response, reducing the peak acceleration associated with signals to provide collapse while increasing displacement capacity. This effect is most pronounced in walls with lower-slenderness ratios, higher precompression, or constraints against uplift and rotation at the top, as differential loading disrupts vertical arching mechanisms that, otherwise, enhance stability under uniform boundary motions. Using only the base signal, a common simplification in seismic assessments fails to capture these differential effects. The results of the simulations are then examined to investigate the largest OOP displacement at which walls can regain stability under dynamic loading, calculating dynamic stability displacement thresholds and showing an average dynamic-to-static stability ratio of 62%, consistent with the 60% ratio used in safety standards. However, deviations occur in walls with failure mechanisms differing from typical flexural behavior. The findings provide critical insights for more accurate seismic assessment and retrofitting of masonry walls by highlighting the importance of considering differential motions. Additionally, this study offers supporting data for the dynamic stability displacement thresholds currently adopted in seismic assessment guidelines, addressing a gap in experimental data and improving the reliability of safety evaluations for unreinforced masonry structures under seismic loading.
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This study investigates the effects of differential support motions, caused by filtering effects due to the building response to earthquakes, on the one-way bending out-of-plane (OOP) behavior of unreinforced brick masonry walls, a factor often overlooked in seismic assessments. A high-fidelity block-based numerical model is used to simulate walls with varying slenderness ratios, precompression levels, and boundary conditions. Floor motions from shake-table tests on two-story masonry buildings with flexible and rigid attic diaphragms under induced and tectonic seismicity are applied at the top and base boundaries of the models as loading signals. Results show that differential motions between supports significantly influence OOP wall response, reducing the peak acceleration associated with signals to provide collapse while increasing displacement capacity. This effect is most pronounced in walls with lower-slenderness ratios, higher precompression, or constraints against uplift and rotation at the top, as differential loading disrupts vertical arching mechanisms that, otherwise, enhance stability under uniform boundary motions. Using only the base signal, a common simplification in seismic assessments fails to capture these differential effects. The results of the simulations are then examined to investigate the largest OOP displacement at which walls can regain stability under dynamic loading, calculating dynamic stability displacement thresholds and showing an average dynamic-to-static stability ratio of 62%, consistent with the 60% ratio used in safety standards. However, deviations occur in walls with failure mechanisms differing from typical flexural behavior. The findings provide critical insights for more accurate seismic assessment and retrofitting of masonry walls by highlighting the importance of considering differential motions. Additionally, this study offers supporting data for the dynamic stability displacement thresholds currently adopted in seismic assessment guidelines, addressing a gap in experimental data and improving the reliability of safety evaluations for unreinforced masonry structures under seismic loading.
Historical buildings in the Netherlands are often founded on shallow, unreinforced foundations atop soft soils such as peat, clay, or loam, making them vulnerable to ground movements. These movements can result from autonomous settlements due to the building’s own weight, or from changes in the soil related to water table variations. Such sources typically induce differential vertical displacements, expressed as ground surface curvature. Movements from deeper sources, such as mining or tunnelling, also cause horizontal displacements or surface strains.
Masonry buildings are sensitive to strains from restrained shrinkage, temperature fluctuations, and soil movements. This study examines façade damage due to a combination of curvature and horizontal strain imposed through the foundations. Non-linear models of masonry façades were placed on a deformable soil block, whose boundaries were manipulated to create targeted combinations of curvature and strain at the surface.
The analysis of various combinations showed that while curvature and horizontal strain each cause damage—manifested as cracks in the masonry—their combination amplifies it. For instance, cracks 1 mm wide appear at a tensile strain of 5e−4 (0.5 mm/m), but when combined with an angular distortion of 1e−3 rad, only half that strain is needed to produce similar damage.
Understanding how curvature and strain interact to damage façades helps define safer deformation limits for vulnerable historical buildings, particularly in areas affected by water table regulation or mining. Additionally, the initial condition of structures must be considered when evaluating their vulnerability to external hazards, including seismic activity. ...
Masonry buildings are sensitive to strains from restrained shrinkage, temperature fluctuations, and soil movements. This study examines façade damage due to a combination of curvature and horizontal strain imposed through the foundations. Non-linear models of masonry façades were placed on a deformable soil block, whose boundaries were manipulated to create targeted combinations of curvature and strain at the surface.
The analysis of various combinations showed that while curvature and horizontal strain each cause damage—manifested as cracks in the masonry—their combination amplifies it. For instance, cracks 1 mm wide appear at a tensile strain of 5e−4 (0.5 mm/m), but when combined with an angular distortion of 1e−3 rad, only half that strain is needed to produce similar damage.
Understanding how curvature and strain interact to damage façades helps define safer deformation limits for vulnerable historical buildings, particularly in areas affected by water table regulation or mining. Additionally, the initial condition of structures must be considered when evaluating their vulnerability to external hazards, including seismic activity. ...
Historical buildings in the Netherlands are often founded on shallow, unreinforced foundations atop soft soils such as peat, clay, or loam, making them vulnerable to ground movements. These movements can result from autonomous settlements due to the building’s own weight, or from changes in the soil related to water table variations. Such sources typically induce differential vertical displacements, expressed as ground surface curvature. Movements from deeper sources, such as mining or tunnelling, also cause horizontal displacements or surface strains.
Masonry buildings are sensitive to strains from restrained shrinkage, temperature fluctuations, and soil movements. This study examines façade damage due to a combination of curvature and horizontal strain imposed through the foundations. Non-linear models of masonry façades were placed on a deformable soil block, whose boundaries were manipulated to create targeted combinations of curvature and strain at the surface.
The analysis of various combinations showed that while curvature and horizontal strain each cause damage—manifested as cracks in the masonry—their combination amplifies it. For instance, cracks 1 mm wide appear at a tensile strain of 5e−4 (0.5 mm/m), but when combined with an angular distortion of 1e−3 rad, only half that strain is needed to produce similar damage.
Understanding how curvature and strain interact to damage façades helps define safer deformation limits for vulnerable historical buildings, particularly in areas affected by water table regulation or mining. Additionally, the initial condition of structures must be considered when evaluating their vulnerability to external hazards, including seismic activity.
Masonry buildings are sensitive to strains from restrained shrinkage, temperature fluctuations, and soil movements. This study examines façade damage due to a combination of curvature and horizontal strain imposed through the foundations. Non-linear models of masonry façades were placed on a deformable soil block, whose boundaries were manipulated to create targeted combinations of curvature and strain at the surface.
The analysis of various combinations showed that while curvature and horizontal strain each cause damage—manifested as cracks in the masonry—their combination amplifies it. For instance, cracks 1 mm wide appear at a tensile strain of 5e−4 (0.5 mm/m), but when combined with an angular distortion of 1e−3 rad, only half that strain is needed to produce similar damage.
Understanding how curvature and strain interact to damage façades helps define safer deformation limits for vulnerable historical buildings, particularly in areas affected by water table regulation or mining. Additionally, the initial condition of structures must be considered when evaluating their vulnerability to external hazards, including seismic activity.
Journal article
(2026)
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Amirhossein Ghezelbash, Alfonso Prosperi, Satyadhrik Sharma, Antonio Maria D’Altri, Jan G. Rots, Francesco Messali
This paper presents a numerical investigation on the effects of settlement-induced pre-damage on the seismic out-of-plane (OOP) response of two-way spanning non-framed unreinforced masonry (URM) walls, investigating also the suitability of static analysis procedures for simulating the dynamic OOP response of pre-damaged walls. For this purpose, the finite-element block-based modeling approach developed and validated by the authors in previous works is employed. URM walls with various geometries and boundary conditions are simulated to investigate the effects of openings and wall-to-diaphragm connections on pre-damage effects. Each specimen is subjected to various settlement profiles, and different levels of obtained settlement-induced damage states are used as initial conditions for OOP analyses. Static and dynamic OOP simulations, the latter considering both induced and tectonic seismicity, and modal analyses are performed. The outputs show that settlement effects on the OOP response emerged as early as the light pre-damage state. Sagging, previously considered in literature less damaging than hogging, caused the greatest OOP stiffness and strength reduction, up to 92% and 80%, respectively. Hogging led to a 60% stiffness and 30% strength drop, particularly in walls with openings. Induced seismicity did not lead to collapse. Static analyses accurately estimated OOP strength and failure mechanisms.
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This paper presents a numerical investigation on the effects of settlement-induced pre-damage on the seismic out-of-plane (OOP) response of two-way spanning non-framed unreinforced masonry (URM) walls, investigating also the suitability of static analysis procedures for simulating the dynamic OOP response of pre-damaged walls. For this purpose, the finite-element block-based modeling approach developed and validated by the authors in previous works is employed. URM walls with various geometries and boundary conditions are simulated to investigate the effects of openings and wall-to-diaphragm connections on pre-damage effects. Each specimen is subjected to various settlement profiles, and different levels of obtained settlement-induced damage states are used as initial conditions for OOP analyses. Static and dynamic OOP simulations, the latter considering both induced and tectonic seismicity, and modal analyses are performed. The outputs show that settlement effects on the OOP response emerged as early as the light pre-damage state. Sagging, previously considered in literature less damaging than hogging, caused the greatest OOP stiffness and strength reduction, up to 92% and 80%, respectively. Hogging led to a 60% stiffness and 30% strength drop, particularly in walls with openings. Induced seismicity did not lead to collapse. Static analyses accurately estimated OOP strength and failure mechanisms.
Predicting Capacity Loss in Settlement-Damaged Masonry Walls under Pushover Loads
An SLA-Based Framework
This study investigates how settlement-induced pre-damage modifies the in-plane pushover response of an unreinforced masonry (URM) wall with a window opening. An event-driven Total Sequentially Linear Analysis (Total-SLA) framework is used. Masonry units are linear elastic, while mortar joints and potential splitting planes are modelled by zero-thickness interface elements capturing tensile opening and frictional sliding through stepwise stiffness/strength reduction. Differential settlement is imposed through a spring-supported base referenced to a prescribed ground profile, and a tensionless condition allows local uplift and partial loss of contact. Settlement-induced damage differs for hogging, sagging, and asymmetric profiles. For the studied wall, sagging and asymmetric settlements reduce the subsequent pushover capacity with peak load reductions up to 25%. Moreover, three bond patterns (stretcher, English, and Flemish) are assessed for the asymmetric settlement case. Stretcher bond maintains a higher post-peak level and recovery, while Flemish bond is intermediate and English bond exhibits the lowest residual resistance after the secondary strength drop.
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This study investigates how settlement-induced pre-damage modifies the in-plane pushover response of an unreinforced masonry (URM) wall with a window opening. An event-driven Total Sequentially Linear Analysis (Total-SLA) framework is used. Masonry units are linear elastic, while mortar joints and potential splitting planes are modelled by zero-thickness interface elements capturing tensile opening and frictional sliding through stepwise stiffness/strength reduction. Differential settlement is imposed through a spring-supported base referenced to a prescribed ground profile, and a tensionless condition allows local uplift and partial loss of contact. Settlement-induced damage differs for hogging, sagging, and asymmetric profiles. For the studied wall, sagging and asymmetric settlements reduce the subsequent pushover capacity with peak load reductions up to 25%. Moreover, three bond patterns (stretcher, English, and Flemish) are assessed for the asymmetric settlement case. Stretcher bond maintains a higher post-peak level and recovery, while Flemish bond is intermediate and English bond exhibits the lowest residual resistance after the secondary strength drop.
This study examines the influence of in-plane (IP) pre-deformations and -damages on the two-way bending out-of-plane (OOP) seismic response of non-framed unreinforced masonry (URM) walls. IP and OOP behaviors of non-framed URM walls are often studied individually and their interaction, such as the effects studied here, remains insufficiently explored. Hence, current design and assessment techniques of non-framed URM walls do not consider the effects of pre-damage and pre-deformation, overestimating safety. This paper addresses this gap. First, a simplified micro-scale numerical modeling approach is developed within Finite Element framework using expanded blocks and zero-thickness interface elements. Shell elements are adopted instead of solid blocks, which are traditionally more common in such studies, to enhance computational efficiency for extensive explorations. Second, the approach is validated against wall IP and OOP experiments, showing good accuracy and reliability. Third, the effects of IP pre-damage and pre-deformation on two-way OOP bending strength and stiffness, called IP/OOP interaction effects, are investigated in a parametric study. The effects of wall openings, IP boundary conditions, vertical pre-compression, and horizontal confinement on interaction effects are investigated. OOP loading is performed at different IP performance states identified via a crack-based approach. According to the results, IP pre-damage or pre-deformation reduced OOP strength between 0% and 30% and OOP stiffness between 30% and 50% for the walls studied in this research and representative of Dutch calcium silicate masonry, emphasizing the importance of accounting for IP/OOP interactions in seismic design and assessment of URM walls. Vertical pre-compression and horizontal confinement are identified as most influential parameters due to their effect on arching mechanisms. Existing analytical models, typically developed for one-way spanning walls, significantly overestimate the loss of OOP performance due to pre-deformation or pre-damage in two-way spanning walls. The study establishes a foundation for structured future research into IP/OOP interaction.
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This study examines the influence of in-plane (IP) pre-deformations and -damages on the two-way bending out-of-plane (OOP) seismic response of non-framed unreinforced masonry (URM) walls. IP and OOP behaviors of non-framed URM walls are often studied individually and their interaction, such as the effects studied here, remains insufficiently explored. Hence, current design and assessment techniques of non-framed URM walls do not consider the effects of pre-damage and pre-deformation, overestimating safety. This paper addresses this gap. First, a simplified micro-scale numerical modeling approach is developed within Finite Element framework using expanded blocks and zero-thickness interface elements. Shell elements are adopted instead of solid blocks, which are traditionally more common in such studies, to enhance computational efficiency for extensive explorations. Second, the approach is validated against wall IP and OOP experiments, showing good accuracy and reliability. Third, the effects of IP pre-damage and pre-deformation on two-way OOP bending strength and stiffness, called IP/OOP interaction effects, are investigated in a parametric study. The effects of wall openings, IP boundary conditions, vertical pre-compression, and horizontal confinement on interaction effects are investigated. OOP loading is performed at different IP performance states identified via a crack-based approach. According to the results, IP pre-damage or pre-deformation reduced OOP strength between 0% and 30% and OOP stiffness between 30% and 50% for the walls studied in this research and representative of Dutch calcium silicate masonry, emphasizing the importance of accounting for IP/OOP interactions in seismic design and assessment of URM walls. Vertical pre-compression and horizontal confinement are identified as most influential parameters due to their effect on arching mechanisms. Existing analytical models, typically developed for one-way spanning walls, significantly overestimate the loss of OOP performance due to pre-deformation or pre-damage in two-way spanning walls. The study establishes a foundation for structured future research into IP/OOP interaction.
Full-field identification of elastic and shear moduli of perforated masonry walls using DIC and stiffness-based shear partition (Euler-Bernoulli vs Timoshenko)
Comparison across clay brick, calcium silicate brick, and calcium silicate block masonry
Digital Image Correlation (DIC) is increasingly used in masonry testing for full-field crack mapping, yet its potential for quantitative identification of elastic properties at structural scale is still not fully exploited for perforated walls where load paths split into multiple piers. This contribution presents a DIC-driven procedure to estimate the Young’s modulus E and the shear modulus G of windowed masonry walls made of three materials: clay brick masonry, calcium silicate brick masonry, and calcium silicate block masonry. Axial strains are extracted at the wall extreme fibres and converted to E using section-dependent bending stresses that account for the reduced cross-section within the window height. For G, pier-average shear strains are obtained from DIC strain fields within defined regions of interest, while pier shear forces are computed by stiffness-based partition of the applied top shear between the left and right piers. Two bounds are considered: Euler–Bernoulli theory (shear-rigid) and Timoshenko theory (shear-flexible) with a shear correction factor. The comparison clarifies how the inferred G depends on pier aspect ratio and the assumed shear deformability. Finally, a parametric study is conducted to quantify how the assumed Poisson’s ratio affects the back-calculation of E from the measured G. The results further indicate that elastic parameters obtained from standard small-scale tests (e.g., prisms or wallets) tend to overestimate the effective E and G inferred at wall scale, which can significantly bias the calibration of continuum and macro-element numerical models.
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Digital Image Correlation (DIC) is increasingly used in masonry testing for full-field crack mapping, yet its potential for quantitative identification of elastic properties at structural scale is still not fully exploited for perforated walls where load paths split into multiple piers. This contribution presents a DIC-driven procedure to estimate the Young’s modulus E and the shear modulus G of windowed masonry walls made of three materials: clay brick masonry, calcium silicate brick masonry, and calcium silicate block masonry. Axial strains are extracted at the wall extreme fibres and converted to E using section-dependent bending stresses that account for the reduced cross-section within the window height. For G, pier-average shear strains are obtained from DIC strain fields within defined regions of interest, while pier shear forces are computed by stiffness-based partition of the applied top shear between the left and right piers. Two bounds are considered: Euler–Bernoulli theory (shear-rigid) and Timoshenko theory (shear-flexible) with a shear correction factor. The comparison clarifies how the inferred G depends on pier aspect ratio and the assumed shear deformability. Finally, a parametric study is conducted to quantify how the assumed Poisson’s ratio affects the back-calculation of E from the measured G. The results further indicate that elastic parameters obtained from standard small-scale tests (e.g., prisms or wallets) tend to overestimate the effective E and G inferred at wall scale, which can significantly bias the calibration of continuum and macro-element numerical models.
Decades of induced seismicity in Groningen have exposed unreinforced clay masonry to frequent, shallow, small-to-moderate earthquakes. Conventional, event-centric vulnerability assessments largely ignore the cumulative effects of repeated shaking and therefore under-predict visible (light, crack-based) damage. We propose a sequence-aware Damage Accumulation Function (DAF) that advances a measured crack-based state Ψ across arbitrary PGV histories by separating similar-intensity repetitions (small increments) from events that set a new maximum (disproportionate jumps). The method integrates (i) earlier full-scale wall and spandrel experiments with high-resolution digital image correlation to quantify crack initiation, widening and extension; (ii) earlier calibrated nonlinear time-history analyses of Groningen-type motions using the Engineering Masonry Model; and (iii) a semi-empirical surrogate linking ∆Ψ to PGV and typological parameters with heteroskedastic, PGV-dependent uncertainty whose incremental contribution decays with sequence position. Applied to historical records and hypothetical futures, DAF results indicate that repeated low-intensity events meaningfully affect accumulation (≈10–20% additional ∆Ψ for same-intensity repeats), while a record-high PGV produces a marked jump. Regional analyses yield exceedance maps that differ from single-event fragility, especially at the edges with low but repeated PGV values and enable decision-facing metrics such as “damage hastening.” The formulation is intended for DS1/early DS2 crack damage of in-plane URM walls and uses PGV as the intensity measure. The DAF provides an interpretable, probabilistic complement to standard fragility where history and repetition govern light-damage progression.
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Decades of induced seismicity in Groningen have exposed unreinforced clay masonry to frequent, shallow, small-to-moderate earthquakes. Conventional, event-centric vulnerability assessments largely ignore the cumulative effects of repeated shaking and therefore under-predict visible (light, crack-based) damage. We propose a sequence-aware Damage Accumulation Function (DAF) that advances a measured crack-based state Ψ across arbitrary PGV histories by separating similar-intensity repetitions (small increments) from events that set a new maximum (disproportionate jumps). The method integrates (i) earlier full-scale wall and spandrel experiments with high-resolution digital image correlation to quantify crack initiation, widening and extension; (ii) earlier calibrated nonlinear time-history analyses of Groningen-type motions using the Engineering Masonry Model; and (iii) a semi-empirical surrogate linking ∆Ψ to PGV and typological parameters with heteroskedastic, PGV-dependent uncertainty whose incremental contribution decays with sequence position. Applied to historical records and hypothetical futures, DAF results indicate that repeated low-intensity events meaningfully affect accumulation (≈10–20% additional ∆Ψ for same-intensity repeats), while a record-high PGV produces a marked jump. Regional analyses yield exceedance maps that differ from single-event fragility, especially at the edges with low but repeated PGV values and enable decision-facing metrics such as “damage hastening.” The formulation is intended for DS1/early DS2 crack damage of in-plane URM walls and uses PGV as the intensity measure. The DAF provides an interpretable, probabilistic complement to standard fragility where history and repetition govern light-damage progression.
This paper investigates the response of one-way spanning unreinforced masonry (URM) walls first statically tilted in the in-plane (IP) and out-of-plane (OOP) directions and then subjected to seismic OOP loading, a subject largely overlooked in the literature. The study is motivated by this knowledge gap and its particular relevance to Netherlands, where ground settlement often leads to visible tilting in buildings, yet sufficient evidence for if and how such tilting should be explicitly considered in design and assessment does not exist. The numerical modeling approach previously proposed by the authors, validated against complex experimental data, is employed in a comprehensive parametric study to provide preliminary insights into the seismic response of tilted walls. The model represents URM unit-by-unit using nonlinear 3D solid expanded blocks and cohesive-frictional zero-thickness joints. Two wall specimens, one short and one long, are subjected to one level of IP base tilting and two levels of OOP base tilting. Static and dynamic OOP loading is then applied while maintaining the prescribed tilt. Under static OOP loading, three levels of vertical pre-compression are considered, representing conditions in low-rise residential buildings. For dynamic OOP analyses, a multi-step loading sequence with varying levels of overburden is used. The results show negligible sensitivity to IP tilting (even up to 4°). While the specimens exhibit slightly greater sensitivity to OOP tilting, primarily due to reduced vertical confinement and increased uplift, responses remain largely stable even with large OOP drift (up to 22% of wall thickness). Aside from the aforementioned findings, this study, being the first one in the literature studying load-bearing tilted walls, highlights key limitations which may have affected the outcomes and emphasizes the need for further research to better understand the behavior of tilted URM walls.
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This paper investigates the response of one-way spanning unreinforced masonry (URM) walls first statically tilted in the in-plane (IP) and out-of-plane (OOP) directions and then subjected to seismic OOP loading, a subject largely overlooked in the literature. The study is motivated by this knowledge gap and its particular relevance to Netherlands, where ground settlement often leads to visible tilting in buildings, yet sufficient evidence for if and how such tilting should be explicitly considered in design and assessment does not exist. The numerical modeling approach previously proposed by the authors, validated against complex experimental data, is employed in a comprehensive parametric study to provide preliminary insights into the seismic response of tilted walls. The model represents URM unit-by-unit using nonlinear 3D solid expanded blocks and cohesive-frictional zero-thickness joints. Two wall specimens, one short and one long, are subjected to one level of IP base tilting and two levels of OOP base tilting. Static and dynamic OOP loading is then applied while maintaining the prescribed tilt. Under static OOP loading, three levels of vertical pre-compression are considered, representing conditions in low-rise residential buildings. For dynamic OOP analyses, a multi-step loading sequence with varying levels of overburden is used. The results show negligible sensitivity to IP tilting (even up to 4°). While the specimens exhibit slightly greater sensitivity to OOP tilting, primarily due to reduced vertical confinement and increased uplift, responses remain largely stable even with large OOP drift (up to 22% of wall thickness). Aside from the aforementioned findings, this study, being the first one in the literature studying load-bearing tilted walls, highlights key limitations which may have affected the outcomes and emphasizes the need for further research to better understand the behavior of tilted URM walls.
Book chapter
(2026)
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Amirhossein Ghezelbash, Alfonso Prosperi, Satyadhrik Sharma, Antonio Maria D’Altri, Jan G. Rots, Francesco Messali
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.
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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.
Out-of-plane seismic behavior of non-framed unreinforced masonry walls with pre-existing seismic damage
Numerical study via a block-based modeling approach
Journal article
(2026)
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Amirhossein Ghezelbash, Satyadhrik Sharma, Antonio Maria D'Altri, Jan G. Rots, Francesco Messali
This paper presents a numerical investigation into the influence of seismic in-plane (IP) pre-damage on the seismic out-of-plane (OOP) response of non-framed unreinforced masonry (URM) walls. These effects, referred to as IP/OOP interaction effects, are rarely investigated for non-framed URM and remain insufficiently understood. Consequently, seismic design and assessment provisions for non-framed URM neglect their potential impact on the vulnerable OOP response of URM. The paper conducts a parametric analysis using the high-fidelity modeling approach developed by the authors and previously validated against the IP and OOP responses of non-framed URM walls. The approach represents URM unit-by-unit via 3D finite-element nonlinear expanded blocks and cohesive-frictional zero-thickness joints. Four wall geometries are considered and pre-damaged by static cyclic IP loading under varying pre-compression levels and boundary conditions. Different IP pre-damage states are used as initial conditions for static and dynamic OOP analyses. Dynamic simulations employ signals representing induced and tectonic earthquakes. OOP stiffness reduction is also tracked through modal analyses. The results show that one-way spanning walls exhibit almost no sensitivity to pre-damage, whereas two-way spanning specimens experience up to 30% and 33% reductions in OOP stiffness and strength at severe pre-damage state. Moreover, under specific conditions, such as opening walls under low pre-compression, does pre-damage alter the OOP failure mechanism and cause more drastic stiffness reductions. Among all configurations, only the pre-damaged one-way spanning walls collapse under induced seismicity, and only at intensities higher than real events. Finally, good agreement is observed between static and dynamic simulations results under pre-damage.
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This paper presents a numerical investigation into the influence of seismic in-plane (IP) pre-damage on the seismic out-of-plane (OOP) response of non-framed unreinforced masonry (URM) walls. These effects, referred to as IP/OOP interaction effects, are rarely investigated for non-framed URM and remain insufficiently understood. Consequently, seismic design and assessment provisions for non-framed URM neglect their potential impact on the vulnerable OOP response of URM. The paper conducts a parametric analysis using the high-fidelity modeling approach developed by the authors and previously validated against the IP and OOP responses of non-framed URM walls. The approach represents URM unit-by-unit via 3D finite-element nonlinear expanded blocks and cohesive-frictional zero-thickness joints. Four wall geometries are considered and pre-damaged by static cyclic IP loading under varying pre-compression levels and boundary conditions. Different IP pre-damage states are used as initial conditions for static and dynamic OOP analyses. Dynamic simulations employ signals representing induced and tectonic earthquakes. OOP stiffness reduction is also tracked through modal analyses. The results show that one-way spanning walls exhibit almost no sensitivity to pre-damage, whereas two-way spanning specimens experience up to 30% and 33% reductions in OOP stiffness and strength at severe pre-damage state. Moreover, under specific conditions, such as opening walls under low pre-compression, does pre-damage alter the OOP failure mechanism and cause more drastic stiffness reductions. Among all configurations, only the pre-damaged one-way spanning walls collapse under induced seismicity, and only at intensities higher than real events. Finally, good agreement is observed between static and dynamic simulations results under pre-damage.
Bacteria-based self-healing agent for masonry crack repair
Assessing watertightness restoration
The preservation and long-term durability of masonry structures, particularly in the context of built heritage, are strongly affected by water ingress. Cracking in mortar joints or at the brick–mortar interface compromises watertightness, accelerates decay mechanisms such as salt crystallisation and freeze–thaw damage, and increases maintenance demands. Traditional repair strategies, such as repointing, are effective but require repeated interventions and monitoring.
In this context, autonomous self-healing mortars are currently gaining increasing attention as a complementary approach to conventional repair. Inspired by developments in self-healing concrete, bacteria-based healing agents have recently been explored for masonry applications. Previous pilot studies demonstrated that a polylactic acid (PLA)-based bacterial agent can promote crack filling in masonry couplets, contributing to aesthetic recovery and partial restoration of bond strength. However, the ability of such systems to restore watertightness, a performance aspect directly linked to durability, has not yet been systematically investigated.
Assessing watertightness recovery in masonry presents methodological challenges. Existing standards typically focus on large-scale wall assemblies or surface water penetration tests, which are not well suited for early-stage material evaluation. Consequently, there is a need for adapted, small-scale methods capable of quantifying changes in permeability associated with cracking and healing. This study addresses this gap by introducing an adapted permeability test derived from research on self-healing concrete and applying it to evaluate watertightness recovery in masonry containing the above-mentioned agent. ...
In this context, autonomous self-healing mortars are currently gaining increasing attention as a complementary approach to conventional repair. Inspired by developments in self-healing concrete, bacteria-based healing agents have recently been explored for masonry applications. Previous pilot studies demonstrated that a polylactic acid (PLA)-based bacterial agent can promote crack filling in masonry couplets, contributing to aesthetic recovery and partial restoration of bond strength. However, the ability of such systems to restore watertightness, a performance aspect directly linked to durability, has not yet been systematically investigated.
Assessing watertightness recovery in masonry presents methodological challenges. Existing standards typically focus on large-scale wall assemblies or surface water penetration tests, which are not well suited for early-stage material evaluation. Consequently, there is a need for adapted, small-scale methods capable of quantifying changes in permeability associated with cracking and healing. This study addresses this gap by introducing an adapted permeability test derived from research on self-healing concrete and applying it to evaluate watertightness recovery in masonry containing the above-mentioned agent. ...
The preservation and long-term durability of masonry structures, particularly in the context of built heritage, are strongly affected by water ingress. Cracking in mortar joints or at the brick–mortar interface compromises watertightness, accelerates decay mechanisms such as salt crystallisation and freeze–thaw damage, and increases maintenance demands. Traditional repair strategies, such as repointing, are effective but require repeated interventions and monitoring.
In this context, autonomous self-healing mortars are currently gaining increasing attention as a complementary approach to conventional repair. Inspired by developments in self-healing concrete, bacteria-based healing agents have recently been explored for masonry applications. Previous pilot studies demonstrated that a polylactic acid (PLA)-based bacterial agent can promote crack filling in masonry couplets, contributing to aesthetic recovery and partial restoration of bond strength. However, the ability of such systems to restore watertightness, a performance aspect directly linked to durability, has not yet been systematically investigated.
Assessing watertightness recovery in masonry presents methodological challenges. Existing standards typically focus on large-scale wall assemblies or surface water penetration tests, which are not well suited for early-stage material evaluation. Consequently, there is a need for adapted, small-scale methods capable of quantifying changes in permeability associated with cracking and healing. This study addresses this gap by introducing an adapted permeability test derived from research on self-healing concrete and applying it to evaluate watertightness recovery in masonry containing the above-mentioned agent.
In this context, autonomous self-healing mortars are currently gaining increasing attention as a complementary approach to conventional repair. Inspired by developments in self-healing concrete, bacteria-based healing agents have recently been explored for masonry applications. Previous pilot studies demonstrated that a polylactic acid (PLA)-based bacterial agent can promote crack filling in masonry couplets, contributing to aesthetic recovery and partial restoration of bond strength. However, the ability of such systems to restore watertightness, a performance aspect directly linked to durability, has not yet been systematically investigated.
Assessing watertightness recovery in masonry presents methodological challenges. Existing standards typically focus on large-scale wall assemblies or surface water penetration tests, which are not well suited for early-stage material evaluation. Consequently, there is a need for adapted, small-scale methods capable of quantifying changes in permeability associated with cracking and healing. This study addresses this gap by introducing an adapted permeability test derived from research on self-healing concrete and applying it to evaluate watertightness recovery in masonry containing the above-mentioned agent.
Temperature variations in masonry façades can induce expansion and contraction movements. When these movements are restrained, cracking and material degradation may occur, especially in older buildings lacking movement or expansion joints. Such temperature variations arise from factors as solar radiation, shading, material color, reflectivity, and environmental conditions. This study investigates the magnitude and spatial distribution of surface temperature variations (ΔT) on exterior masonry wall surfaces using outdoor infrared (IR) thermography. A better understanding of the magnitude and distribution of ΔT is essential for accurate damage assessment and for improving the attributability of observed damage to temperature effects rather than to other causes. Field data were collected in Delft, the Netherlands. Thermal images were captured with an IR camera to identify temperature differences across various points on exterior wall surfaces under direct solar radiation and varying shading conditions. The acquired imagery was analyzed using temperature histograms and profiles to quantify thermal gradients over the surface area of the façades. Results revealed significant spatial temperature variations, with measured ΔT values reaching up to 13 °C between the warmest and coolest zones on individual façades. Even where façades showed no pronounced surface gradients, temperature differences of up to 6 °C occurred between different, contiguous exterior walls of the same building. The study demonstrates that outdoor thermography, combined with targeted image processing, effectively identifies thermal gradients on masonry façades. These gradients reflect uneven thermal responses under real environmental conditions, which can accelerate moisture-related damage, cracking, and material fatigue. The findings emphasize the need to account for surface temperature heterogeneity in damage assessment of existing structures.
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Temperature variations in masonry façades can induce expansion and contraction movements. When these movements are restrained, cracking and material degradation may occur, especially in older buildings lacking movement or expansion joints. Such temperature variations arise from factors as solar radiation, shading, material color, reflectivity, and environmental conditions. This study investigates the magnitude and spatial distribution of surface temperature variations (ΔT) on exterior masonry wall surfaces using outdoor infrared (IR) thermography. A better understanding of the magnitude and distribution of ΔT is essential for accurate damage assessment and for improving the attributability of observed damage to temperature effects rather than to other causes. Field data were collected in Delft, the Netherlands. Thermal images were captured with an IR camera to identify temperature differences across various points on exterior wall surfaces under direct solar radiation and varying shading conditions. The acquired imagery was analyzed using temperature histograms and profiles to quantify thermal gradients over the surface area of the façades. Results revealed significant spatial temperature variations, with measured ΔT values reaching up to 13 °C between the warmest and coolest zones on individual façades. Even where façades showed no pronounced surface gradients, temperature differences of up to 6 °C occurred between different, contiguous exterior walls of the same building. The study demonstrates that outdoor thermography, combined with targeted image processing, effectively identifies thermal gradients on masonry façades. These gradients reflect uneven thermal responses under real environmental conditions, which can accelerate moisture-related damage, cracking, and material fatigue. The findings emphasize the need to account for surface temperature heterogeneity in damage assessment of existing structures.
Historical masonry façades are susceptible to variations in temperature. This is because their movements—expansion caused by an increase in temperature or contraction by a decrease—are restrained by other structural elements. To analyse these effects, models typically assign a prescribed strain to the façade while enforcing a rigid boundary at the foundation (or the floors, if they are rigid). More advanced models include the foundation, with a stiffness different from that of the façade and no prescribed strain, as the restraining element. This leads to conservative estimations of damage since the restraining effect is large. Indeed, these models can be further improved. A temperature gradient across the façade, including the foundation, can produce more gradual strains in the material and thus less damage. For this study, the improvements consider the inclusion of the soil underneath the building. A realistic temperature gradient for a sunny summer day or a chilly winter night, including a gradient over the foundation and into the soil, is applied. The restraining effects are provided by the soil and the temperature gradients. In this manner, the consequences of temperature variations on clay-brick masonry façades are investigated. The models reveal that damage, observed as cracking in the non-linear masonry model, is significantly reduced when applying the more gradual temperature profiles. Moreover, the damage patterns observed are different from those obtained from a simpler model. This is an important observation since crack patterns are sometimes employed to determine the origin of the damage. Furthermore, the type of soil also plays a role in the intensity of damage observed for identical temperature profiles. Softer soils, such as clay, peat, or loam, provide less restraint than stiffer soils like sand. Hence, façades on softer soils are less likely to develop damage from temperature variations.
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Historical masonry façades are susceptible to variations in temperature. This is because their movements—expansion caused by an increase in temperature or contraction by a decrease—are restrained by other structural elements. To analyse these effects, models typically assign a prescribed strain to the façade while enforcing a rigid boundary at the foundation (or the floors, if they are rigid). More advanced models include the foundation, with a stiffness different from that of the façade and no prescribed strain, as the restraining element. This leads to conservative estimations of damage since the restraining effect is large. Indeed, these models can be further improved. A temperature gradient across the façade, including the foundation, can produce more gradual strains in the material and thus less damage. For this study, the improvements consider the inclusion of the soil underneath the building. A realistic temperature gradient for a sunny summer day or a chilly winter night, including a gradient over the foundation and into the soil, is applied. The restraining effects are provided by the soil and the temperature gradients. In this manner, the consequences of temperature variations on clay-brick masonry façades are investigated. The models reveal that damage, observed as cracking in the non-linear masonry model, is significantly reduced when applying the more gradual temperature profiles. Moreover, the damage patterns observed are different from those obtained from a simpler model. This is an important observation since crack patterns are sometimes employed to determine the origin of the damage. Furthermore, the type of soil also plays a role in the intensity of damage observed for identical temperature profiles. Softer soils, such as clay, peat, or loam, provide less restraint than stiffer soils like sand. Hence, façades on softer soils are less likely to develop damage from temperature variations.
Extracting cores with diameters of 100 to 150 mm from masonry structures has emerged as a novel, less destructive method for assessing the mechanical properties of masonry units, particularly their compressive strength. Unlike traditional methods, such as using larger wallets, this approach requires less material and causes minimal damage to the original structure, which is critical when dealing with historical buildings. However, to obtain consistent and reliable results, certain parameters, specifically the dimensions of the core cap, must be carefully defined, as they significantly influence the overall behaviour of the samples. The study employs a detailed block-based modelling approach, incorporating zero-thickness cohesive elements at the brick-mortar interfaces. Additionally, tangential and normal contact interactions were defined between the cap and core components. The concrete damage plasticity (CDP) model, implemented in ABAQUS, has been adopted as the constitutive model to account for the nonlinear behaviour of brick, mortar, and cap. The results indicate that the length of the cap has a more pronounced effect on the sample’s mechanical behaviour than its height. Additionally, the study investigates the mechanical properties of the interface between the cap and the core, identifying friction and normal stiffness as critical factors. These findings provide valuable insights for optimizing the core capping process and improving the reliability of masonry mechanical property assessments, particularly in the preservation of historical structures.
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Extracting cores with diameters of 100 to 150 mm from masonry structures has emerged as a novel, less destructive method for assessing the mechanical properties of masonry units, particularly their compressive strength. Unlike traditional methods, such as using larger wallets, this approach requires less material and causes minimal damage to the original structure, which is critical when dealing with historical buildings. However, to obtain consistent and reliable results, certain parameters, specifically the dimensions of the core cap, must be carefully defined, as they significantly influence the overall behaviour of the samples. The study employs a detailed block-based modelling approach, incorporating zero-thickness cohesive elements at the brick-mortar interfaces. Additionally, tangential and normal contact interactions were defined between the cap and core components. The concrete damage plasticity (CDP) model, implemented in ABAQUS, has been adopted as the constitutive model to account for the nonlinear behaviour of brick, mortar, and cap. The results indicate that the length of the cap has a more pronounced effect on the sample’s mechanical behaviour than its height. Additionally, the study investigates the mechanical properties of the interface between the cap and the core, identifying friction and normal stiffness as critical factors. These findings provide valuable insights for optimizing the core capping process and improving the reliability of masonry mechanical property assessments, particularly in the preservation of historical structures.
Non-proportional sequentially-linear analysis for masonry structures
Capturing combined foundation settlement and pushover loads
Unreinforced masonry (URM) walls are highly sensitive to non-proportional loading histories, particularly when foundation settlement precedes lateral loading. In such cases, pre-damage induced by settlement can significantly affect the subsequent structural response and cannot be adequately represented using proportional loading assumptions or equivalent reduction factors.
A Total Sequentially Linear Analysis (Total SLA) framework is developed to investigate the combined effects of boundary conditions, geometry, and settlement-induced pre-damage on the pushover response of URM walls. The numerical model represents masonry units as linear elastic continua and concentrates nonlinearity within zero-thickness interface elements governed by discrete damage modes. Settlement and pushover are applied sequentially within a unified event-driven formulation, allowing damage states to be inherited across loading stages.
The results show that the initial elastic response is largely insensitive to the top boundary conditions, whereas significant differences emerge during the softening phase. Fixed-top configurations exhibit a more gradual degradation of stiffness. Cantilever and free-top conditions, in contrast, show sliding-dominated behavior. Settlement causes irreversible damage, reducing both stiffness and peak capacity during subsequent pushover loading. The effects are amplified in walls with openings. These results demonstrate that neglecting load-path dependency may lead to inaccurate predictions of stiffness degradation and peak capacity in URM walls. ...
A Total Sequentially Linear Analysis (Total SLA) framework is developed to investigate the combined effects of boundary conditions, geometry, and settlement-induced pre-damage on the pushover response of URM walls. The numerical model represents masonry units as linear elastic continua and concentrates nonlinearity within zero-thickness interface elements governed by discrete damage modes. Settlement and pushover are applied sequentially within a unified event-driven formulation, allowing damage states to be inherited across loading stages.
The results show that the initial elastic response is largely insensitive to the top boundary conditions, whereas significant differences emerge during the softening phase. Fixed-top configurations exhibit a more gradual degradation of stiffness. Cantilever and free-top conditions, in contrast, show sliding-dominated behavior. Settlement causes irreversible damage, reducing both stiffness and peak capacity during subsequent pushover loading. The effects are amplified in walls with openings. These results demonstrate that neglecting load-path dependency may lead to inaccurate predictions of stiffness degradation and peak capacity in URM walls. ...
Unreinforced masonry (URM) walls are highly sensitive to non-proportional loading histories, particularly when foundation settlement precedes lateral loading. In such cases, pre-damage induced by settlement can significantly affect the subsequent structural response and cannot be adequately represented using proportional loading assumptions or equivalent reduction factors.
A Total Sequentially Linear Analysis (Total SLA) framework is developed to investigate the combined effects of boundary conditions, geometry, and settlement-induced pre-damage on the pushover response of URM walls. The numerical model represents masonry units as linear elastic continua and concentrates nonlinearity within zero-thickness interface elements governed by discrete damage modes. Settlement and pushover are applied sequentially within a unified event-driven formulation, allowing damage states to be inherited across loading stages.
The results show that the initial elastic response is largely insensitive to the top boundary conditions, whereas significant differences emerge during the softening phase. Fixed-top configurations exhibit a more gradual degradation of stiffness. Cantilever and free-top conditions, in contrast, show sliding-dominated behavior. Settlement causes irreversible damage, reducing both stiffness and peak capacity during subsequent pushover loading. The effects are amplified in walls with openings. These results demonstrate that neglecting load-path dependency may lead to inaccurate predictions of stiffness degradation and peak capacity in URM walls.
A Total Sequentially Linear Analysis (Total SLA) framework is developed to investigate the combined effects of boundary conditions, geometry, and settlement-induced pre-damage on the pushover response of URM walls. The numerical model represents masonry units as linear elastic continua and concentrates nonlinearity within zero-thickness interface elements governed by discrete damage modes. Settlement and pushover are applied sequentially within a unified event-driven formulation, allowing damage states to be inherited across loading stages.
The results show that the initial elastic response is largely insensitive to the top boundary conditions, whereas significant differences emerge during the softening phase. Fixed-top configurations exhibit a more gradual degradation of stiffness. Cantilever and free-top conditions, in contrast, show sliding-dominated behavior. Settlement causes irreversible damage, reducing both stiffness and peak capacity during subsequent pushover loading. The effects are amplified in walls with openings. These results demonstrate that neglecting load-path dependency may lead to inaccurate predictions of stiffness degradation and peak capacity in URM walls.
Journal article
(2026)
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Yopi P. Oktiovan, Francesco Messali, Bora Pulatsu, Satyadhrik Sharma, José V. Lemos, Jan G. Rots
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.
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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.
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.
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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.
Aspects To Consider When Modelling the Response of Masonry Façades to Ground Movements
Lessons From A Few Studies
In the Netherlands, quasi-static soil movements from subsidence/consolidation are a major cause of differential settlements and crack damage in masonry façades and buildings. Recent studies have clarified where modelling gives reliable insight and where it misleads. The paper presents these insights as a checklist. Key aspects include façade geometry and its effect on crack patterns and deformation transfer, the distinction between greenfield and building deformations, explicit representation of soil–foundation–façade interaction, small-strain soil stiffness and progressive nonlinearity, masonry cracking and stiffness loss, and the role of initial damage and foundation behaviour. Systematic variations are needed to quantify uncertainty.
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In the Netherlands, quasi-static soil movements from subsidence/consolidation are a major cause of differential settlements and crack damage in masonry façades and buildings. Recent studies have clarified where modelling gives reliable insight and where it misleads. The paper presents these insights as a checklist. Key aspects include façade geometry and its effect on crack patterns and deformation transfer, the distinction between greenfield and building deformations, explicit representation of soil–foundation–façade interaction, small-strain soil stiffness and progressive nonlinearity, masonry cracking and stiffness loss, and the role of initial damage and foundation behaviour. Systematic variations are needed to quantify uncertainty.
Seasonal changes, climate, and human activities can cause groundwater fluctuations, leading to differential settlements. Unreinforced masonry (URM) buildings are vulnerable to differential settlements due to low tensile strength and quasi-brittle behaviour. Damage prediction requires a better understanding of the interaction between structure, foundation, soil, and settlement causes. While previous studies focused on tunnelling or excavation, this study examines damage from progressive groundwater lowering using non-linear finite element (NLFE) modelling in DIANA FEA. The analysis employs a two-step approach. First, a 3D ground-only model is used to calculate the free-field (or “greenfield”) horizontal strain εh and angular distortion β, well-established metrics in previous tunnelling, excavation, and mining studies, under an imposed groundwater lowering scenario. This step establishes a baseline to assess how the presence of the building alters the greenfield εh and β through soil-structure interaction. Then, a 3D coupled model incorporating the URM building and its shallow foundation is used to evaluate the effects on displacements and damage.
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Seasonal changes, climate, and human activities can cause groundwater fluctuations, leading to differential settlements. Unreinforced masonry (URM) buildings are vulnerable to differential settlements due to low tensile strength and quasi-brittle behaviour. Damage prediction requires a better understanding of the interaction between structure, foundation, soil, and settlement causes. While previous studies focused on tunnelling or excavation, this study examines damage from progressive groundwater lowering using non-linear finite element (NLFE) modelling in DIANA FEA. The analysis employs a two-step approach. First, a 3D ground-only model is used to calculate the free-field (or “greenfield”) horizontal strain εh and angular distortion β, well-established metrics in previous tunnelling, excavation, and mining studies, under an imposed groundwater lowering scenario. This step establishes a baseline to assess how the presence of the building alters the greenfield εh and β through soil-structure interaction. Then, a 3D coupled model incorporating the URM building and its shallow foundation is used to evaluate the effects on displacements and damage.
Journal article
(2026)
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Yopi P. Oktiovan, José V. Lemos, Bora Pulatsu, Francesco Messali, Jan G. Rots, Daniele Malomo
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.
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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.