The present work aims to expand the knowledge of the behaviour of masonry corners, which are capital to obtain an integral seismic response in masonry buildings. In particular, the influence of the seismic load orientation (from π/4 to π/2) is investigated experimentally, numerically and analytically. Both units and interfaces have been subjected to a material characterisation process, following which pseudo-static 1:4 scaled experiments on a tilting table have been conducted on a symmetric dry-joint masonry corner. The experimental results have also been simulated using a discrete element model. Finally, a new analytical limit analysis model has been developed, which considers both experimental and numerical observations and accounts for rocking-sliding and flexural mechanisms. In general, a good agreement is found between the three approaches, both in terms of collapse mechanism and load multiplier.@en

The Cathedral of Ica, Peru, is one of the four prototype buildings involved in the ongoing Seismic Retrofitting Project, initiative of the Getty Conservation Institute. The complex historical building, which was heavily damaged by earthquakes in 2007 and 2009, can be divided into two substructures: an external masonry envelope and an internal timber frame built by a construction method known as quincha technique. This study makes use of the information available in literature and the results obtained from experimental campaigns performed by Pontificia Universidad Católica del Perú and University of Minho. Nonlinear behaviour of masonry is simulated in the numerical models by considering specified compressive and tensile softening behaviour, while isotropic homogeneous and linear behaviour is adopted for modelling timber with appropriate assumptions on the connections. A single representative bay was initially studied by performing linear elastic analysis and verifying the compliance with the various criteria specified by the applicable normative to discuss the actual failure of Ica Cathedral. Afterwards, the structural behaviour of the two substructures composing the Cathedral is evaluated independently. Finally, the interaction of these two substructures is investigated by performing structural analysis on the entire structure of Ica Cathedral. Several structural analysis techniques, including eigenvalue, nonlinear static and dynamic analyses, are performed in order to: (1) evaluate the dominant mode shapes of the structure; (2) validate the numerical models by reproducing the structural damage observed in situ; (3) estimate the structural performance; and (4) identify the main failure mechanisms.@en

Near Surface Mounted (NSM) reinforcement is an interesting technique for seismic strengthening of masonry and historical structures. Despite having several advantages compared to conventional techniques, little attention has been given to understanding the involved mechanisms (such as bond behavior) in the performance of masonry components strengthened with this reinforcement technique. This study presents an experimental and analytical investigation on the bond performance of NSM-strengthened masonry bricks aiming at filling the existing gaps in the available experimental results in the literature. The main focus is on the effect of test setup and bond length, but attention has also been given to the groove size and loading regime effect on the bond performance. The accuracy of the existing bond strength prediction models is also assessed and the required modifications are proposed.@en

This paper presents a benchmark exercise for the seismic assessment of unreinforced masonry (URM) buildings as a follow-up of a blind prediction test organized in the context of the European Conference of Earthquake Engineering Series. The blind prediction exercise was aimed at better defining the open issues in current procedures for modeling and performing seismic analysis of URM buildings, by highlighting the uncertainty that can influence the results. This work presents an overview of the approaches used by different research teams and the scope of predictions. The benchmark structure was a three-story building with traditional European architecture from which two Cases were considered: A) stone masonry walls and flexible horizontal diaphragms and B) brick masonry walls and rigid horizontal diaphragms. A wide range of approaches was used by the participating teams concerning modeling strategies, methods of analysis and criteria for the attainment of limit states, which are here addressed as potential sources for the dispersion of predictions. The results were compared in terms of capacity curves, predicted failure mechanisms compatible with the fulfillment of limit states of near collapse and damage limitation, and related minimum values of peak ground acceleration (PGA). The results show an overall good agreement for damage patterns and collapse mechanisms in both benchmark structures, presenting some differences in the type of failure mode and its extent. However, the scatter of predicted capacity curves and critical PGAs is very high, especially for the Case with brick masonry and rigid diaphragms, indicating that clearer procedures in the building codes are required for professionals.@en

This paper presents a benchmark exercise for the seismic assessment of unreinforced masonry (URM) buildings as a follow-up of a blind prediction test organized in the context of the European Conference of Earthquake Engineering Series. The blind prediction exercise was aimed at better defining the open issues in current procedures for modeling and performing seismic analysis of URM buildings, by highlighting the uncertainty that can influence the results. This work presents an overview of the approaches used by different research teams and the scope of predictions. The benchmark structure was a three-story building with traditional European architecture from which two Cases were considered: A) stone masonry walls and flexible horizontal diaphragms and B) brick masonry walls and rigid horizontal diaphragms. A wide range of approaches was used by the participating teams concerning modeling strategies, methods of analysis and criteria for the attainment of limit states, which are here addressed as potential sources for the dispersion of predictions. The results were compared in terms of capacity curves, predicted failure mechanisms compatible with the fulfillment of limit states of near collapse and damage limitation, and related minimum values of peak ground acceleration (PGA). The results show an overall good agreement for damage patterns and collapse mechanisms in both benchmark structures, presenting some differences in the type of failure mode and its extent. However, the scatter of predicted capacity curves and critical PGAs is very high, especially for the Case with brick masonry and rigid diaphragms, indicating that clearer procedures in the building codes are required for professionals.@en

This paper presents a benchmark exercise for the seismic assessment of unreinforced masonry (URM) buildings as a follow-up of a blind prediction test organized in the context of the European Conference of Earthquake Engineering Series. The blind prediction exercise was aimed at better defining the open issues in current procedures for modeling and performing seismic analysis of URM buildings, by highlighting the uncertainty that can influence the results. This work presents an overview of the approaches used by different research teams and the scope of predictions. The benchmark structure was a three-story building with traditional European architecture from which two Cases were considered: A) stone masonry walls and flexible horizontal diaphragms and B) brick masonry walls and rigid horizontal diaphragms. A wide range of approaches was used by the participating teams concerning modeling strategies, methods of analysis and criteria for the attainment of limit states, which are here addressed as potential sources for the dispersion of predictions. The results were compared in terms of capacity curves, predicted failure mechanisms compatible with the fulfillment of limit states of near collapse and damage limitation, and related minimum values of peak ground acceleration (PGA). The results show an overall good agreement for damage patterns and collapse mechanisms in both benchmark structures, presenting some differences in the type of failure mode and its extent. However, the scatter of predicted capacity curves and critical PGAs is very high, especially for the Case with brick masonry and rigid diaphragms, indicating that clearer procedures in the building codes are required for professionals.@en

Masonry structures have been observed to display a high vulnerability to failure under seismic action. This stems from the fact that their structural configurations usually lack adequate connections among the distinct elements, resulting in the formation of local mechanisms experiencing Out-Of-Plane (OOP) collapse. In this context, rocking dynamics has proven to be a valuable methodology for the analysis of masonry walls. Classical rocking theory can provide a fast solution to the dynamic phenomena taking place if simple configurations are examined. Nevertheless, as the degrees of freedom and the boundary conditions increase, the complexity increases, and thus the classical rocking theory becomes impractical. In the meantime, recent developments in computational modelling of masonry structures are gaining significant attraction. This includes block-based models which inherently consider the complexity of the problem and enable the solution to be obtained easily in the discretised spatial and time domains. However, despite their widespread use, applications of such models usually lack a reliable treatment of damping. The present work attempts to bridge the gap between the well-established energy loss of the classical rocking theory and the treatment of damping of block-based computational models. To do so, the dynamics of the problem are reviewed and an equivalent viscous damping model is proposed. A unilateral dashpot formulation allows the replication of the impulsive nature of the energy loss at impact. Afterwards, a calibration methodology is adopted for the practical range of the problem's parameters and a ready-to-use equation is provided, which respects energy equivalence. The performance of the proposed damping model is also evaluated through comparisons with experimental results.@en

Masonry structures have been observed to display a high vulnerability to failure under seismic action. This stems from the fact that their structural configurations usually lack adequate connections among the distinct elements, resulting in the formation of local mechanisms experiencing Out-Of-Plane (OOP) collapse. In this context, rocking dynamics has proven to be a valuable methodology for the analysis of masonry walls. Classical rocking theory can provide a fast solution to the dynamic phenomena taking place if simple configurations are examined. Nevertheless, as the degrees of freedom and the boundary conditions increase, the complexity increases, and thus the classical rocking theory becomes impractical. In the meantime, recent developments in computational modelling of masonry structures are gaining significant attraction. This includes block-based models which inherently consider the complexity of the problem and enable the solution to be obtained easily in the discretised spatial and time domains. However, despite their widespread use, applications of such models usually lack a reliable treatment of damping. The present work attempts to bridge the gap between the well-established energy loss of the classical rocking theory and the treatment of damping of block-based computational models. To do so, the dynamics of the problem are reviewed and an equivalent viscous damping model is proposed. A unilateral dashpot formulation allows the replication of the impulsive nature of the energy loss at impact. Afterwards, a calibration methodology is adopted for the practical range of the problem's parameters and a ready-to-use equation is provided, which respects energy equivalence. The performance of the proposed damping model is also evaluated through comparisons with experimental results.@en

Masonry structures have been observed to display a high vulnerability to failure under seismic action. This stems from the fact that their structural configurations usually lack adequate connections among the distinct elements, resulting in the formation of local mechanisms experiencing Out-Of-Plane (OOP) collapse. In this context, rocking dynamics has proven to be a valuable methodology for the analysis of masonry walls. Classical rocking theory can provide a fast solution to the dynamic phenomena taking place if simple configurations are examined. Nevertheless, as the degrees of freedom and the boundary conditions increase, the complexity increases, and thus the classical rocking theory becomes impractical. In the meantime, recent developments in computational modelling of masonry structures are gaining significant attraction. This includes block-based models which inherently consider the complexity of the problem and enable the solution to be obtained easily in the discretised spatial and time domains. However, despite their widespread use, applications of such models usually lack a reliable treatment of damping. The present work attempts to bridge the gap between the well-established energy loss of the classical rocking theory and the treatment of damping of block-based computational models. To do so, the dynamics of the problem are reviewed and an equivalent viscous damping model is proposed. A unilateral dashpot formulation allows the replication of the impulsive nature of the energy loss at impact. Afterwards, a calibration methodology is adopted for the practical range of the problem's parameters and a ready-to-use equation is provided, which respects energy equivalence. The performance of the proposed damping model is also evaluated through comparisons with experimental results.@en

Unreinforced masonry structures, particularly façade walls, are seismically vulnerable due to their weak connections with adjacent walls, floors, and/or roofs. During an earthquake, such walls formulate local mechanisms prone to out-of-plane collapse. This behavior has been largely investigated using classical rocking theory, which assumes the structure responds as a rigid body undergoing rocking motion, with energy dissipation at impact. Due to the complexity of the problem, however, e.g., number of degrees of freedom or boundary conditions, numerical block-based modeling is gaining momentum. However, numerical models lack a consistent and reliable treatment of the energy loss at impact. This paper bridges the gap between the well-established energy loss of classical rocking theory and the treatment of damping in numerical modeling. Specifically, it proposes an equivalent viscous damping model through novel ready-to-use predictive equations that capture the dissipative phenomena during both one-sided and two-sided planar rocking motion. The results reveal a satisfactory performance of the proposed model through comparisons with experimental results from literature and highlight its universality and robustness through applications of the model in fundamentally different block-based numerical modeling software.@en

This paper presents a user-friendly, CAD-interfaced methodology for the rapid seismic assessment of historic masonry structures. The proposed multi-level procedure consists of a two-step analysis that combines upper bound limit analysis with non-linear dynamic (rocking) analysis to solve for seismic collapse in a computationally-efficient manner. In the first step, the failure mechanisms are defined by means of parameterization of the failure surfaces. Hence, the upper bound limit theorem of the limit analysis, coupled with a heuristic solver, is subsequently adopted to search for the load multiplier’s minimum value and the macro-block geometry. In the second step, the kinematic constants defining the rocking equation of motion are automatically computed for the refined macro-block model, which can be solved for representative time-histories. The proposed methodology has been entirely integrated in the user-friendly visual programming environment offered by Rhinoceros3D + Grasshopper, allowing it to be used by students, researchers and practicing structural engineers. Unlike time-consuming advanced methods of analysis, the proposed method allows users to perform a seismic assessment of masonry buildings in a rapid and computationally-efficient manner. Such an approach is particularly useful for territorial scale vulnerability analysis (e.g., for risk assessment and mitigation historic city centres) or as post-seismic event response (when the safety and stability of a large number of buildings need to be assessed with limited resources). The capabilities of the tool are demonstrated by comparing its predictions with those arising from the literature as well as from code-based assessment methods for three case studies.@en

This paper presents a user-friendly, CAD-interfaced methodology for the rapid seismic assessment of historic masonry structures. The proposed multi-level procedure consists of a two-step analysis that combines upper bound limit analysis with non-linear dynamic (rocking) analysis to solve for seismic collapse in a computationally-efficient manner. In the first step, the failure mechanisms are defined by means of parameterization of the failure surfaces. Hence, the upper bound limit theorem of the limit analysis, coupled with a heuristic solver, is subsequently adopted to search for the load multiplier’s minimum value and the macro-block geometry. In the second step, the kinematic constants defining the rocking equation of motion are automatically computed for the refined macro-block model, which can be solved for representative time-histories. The proposed methodology has been entirely integrated in the user-friendly visual programming environment offered by Rhinoceros3D + Grasshopper, allowing it to be used by students, researchers and practicing structural engineers. Unlike time-consuming advanced methods of analysis, the proposed method allows users to perform a seismic assessment of masonry buildings in a rapid and computationally-efficient manner. Such an approach is particularly useful for territorial scale vulnerability analysis (e.g., for risk assessment and mitigation historic city centres) or as post-seismic event response (when the safety and stability of a large number of buildings need to be assessed with limited resources). The capabilities of the tool are demonstrated by comparing its predictions with those arising from the literature as well as from code-based assessment methods for three case studies.@en

This paper presents a user-friendly, CAD-interfaced methodology for the rapid seismic assessment of historic masonry structures. The proposed multi-level procedure consists of a two-step analysis that combines upper bound limit analysis with non-linear dynamic (rocking) analysis to solve for seismic collapse in a computationally-efficient manner. In the first step, the failure mechanisms are defined by means of parameterization of the failure surfaces. Hence, the upper bound limit theorem of the limit analysis, coupled with a heuristic solver, is subsequently adopted to search for the load multiplier’s minimum value and the macro-block geometry. In the second step, the kinematic constants defining the rocking equation of motion are automatically computed for the refined macro-block model, which can be solved for representative time-histories. The proposed methodology has been entirely integrated in the user-friendly visual programming environment offered by Rhinoceros3D + Grasshopper, allowing it to be used by students, researchers and practicing structural engineers. Unlike time-consuming advanced methods of analysis, the proposed method allows users to perform a seismic assessment of masonry buildings in a rapid and computationally-efficient manner. Such an approach is particularly useful for territorial scale vulnerability analysis (e.g., for risk assessment and mitigation historic city centres) or as post-seismic event response (when the safety and stability of a large number of buildings need to be assessed with limited resources). The capabilities of the tool are demonstrated by comparing its predictions with those arising from the literature as well as from code-based assessment methods for three case studies.@en