Bed joint reinforced repointing is a retrofitting technique for unreinforced masonry structures that is commonly applied in the Netherlands to repair settlement-induced damage. Using this technique, the bed joints of masonry walls are reinforced with steel rebars that are embedded in a high strength repair mortar. Due to the increase of induced seismic events in the northern part of the Netherlands, an experimental study was carried out at Delft University of Technology to investigate the performance of this retrofitting technique for combined settlement and seismic loading. This paper aims to simulate the experimental results, with a focus on the comparison of different finite element modelling approaches for studying both un-strengthened and strengthened full-scale tested walls. To that end, three different models are investigated – comprising both macro (continuum) and simplified and detailed micro (brick-to-brick) modelling approaches. The bricks and mortar joints are modelled as one homogenous continuum in the macro model, whereas in the two brick-to-brick models these structural components are modelled separately, with the detailed model including interface elements to simulate the brick–mortar bonds. Nonlinear pushover analyses are subsequently carried out using all three modelling approaches, for both monotonic and cyclic loading cases. Based on these analyses, the detailed brick-to-brick model was found unsuitable to simulate the strengthened wall because cracks in the model mainly occur in the form of opening of the brick–mortar bond interfaces, while smeared cracking in the plane stress elements of the mortar joints is very limited. Similarly, the continuum damage model was found to be inaccurate when pre-existing damage in the experiment needed to be taken into account. The continuum damage model also showed lower axial stresses in the rebars, compared with the simplified brick-to-brick model, as the former does not allow for the direct assignment of material properties for the high strength repair mortar in the strengthened joints.

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This work compares the ability of different numerical modelling approaches to simulate the out-of-plane behaviour of two-leaf stone masonry walls with different masonry bond configurations: an irregular drystone stone masonry wall and a masonry wall with roughly cut regular stone units. Finite element modelling, considering both a micro and macro-modelling approach, and the distinct element method have been compared in this study, which intends to (i) provide an insight regarding parameter estimation and the calibration procedure for each modelling approach considered; (ii) highlight their pros and cons of the selected modelling strategies; (iii) further expand the existing literature addressing the numerical modelling of two-leaf stone masonry walls.

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

One of the characteristic features of the city of Utrecht is its extensive system of canals and wharf cellars, whose constructions date back as early as the 1200s, and which are now considered as one of the historical properties of the city. A typical wharf cellar in Utrecht comprises a masonry barrel vault with multi-layered rings for the cellar interior, masonry piers which are interconnected to the other wharf cellars, and spandrel walls for the façades. Due to increased traffic volume and urbanization which caused the increase of dead load and traffic load, it is important to assess the structural safety and state of maintenance of these historical structures. In this paper, a novel safety assessment framework for these structures is presented and applied to the analysis of a typical masonry wharf cellar in central Utrecht. The geometry of the cellar is first parametrically generated, which is then used to create a block-based numerical model for analysis using the Distinct Element Method (DEM), where bricks units are modelled as discrete blocks separated by zero thickness interfaces. Traffic loads in accordance with the Dutch Standard traffic model for regular vehicles and emergency service vehicles are calculated and the dispersion through the filling soil is modelled. The ultimate load due to these load configurations is then assessed. The analysis results can be used to identify the critical load cases and the failure mechanisms of the wharf cellar, while also providing general insights into the safety and stability of the cellars, thus aiding engineers in their efforts to extend the lifespan of these historical structures.@en

Failure of tall slender masonry structures during earthquakes often involves partial collapse of the structure well-above ground level. Consequently, the elastic response of the structure needs to be considered, which often requires modal analysis using finite element models — the generation of which can be labour-intensive and time-consuming. This paper presents a new integrated modelling approach which combines finite element analysis with rocking dynamics to model the seismic response of complex structural geometries in a computationally-efficient manner. The modelling strategy is implemented within the open-source computational framework COMPAS and is incorporated within the broader framework of a tool being developed for the seismic collapse assessment of masonry structures. The framework of this tool is first outlined, and the utility of the new modelling approach then demonstrated through application to the seismic assessment of a three historic masonry towers in North-Eastern Italy. The importance of accounting for elastic amplification effects, as well as the influence of varying boundary conditions on the dynamic response, is also illustrated.

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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

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.

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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.

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A blind prediction contest was organized to evaluate the ability of different modeling approaches to simulate the seismic rocking response of a full-scale four-column podium structure. The structure was tested on a shake table, and was subjected to two bidirectional ground motion ensembles comprising 100 synthetic records each. This short communication presents the main assumptions and results from the model, developed using the distinct element method, which provided the second-best prediction of the experimental results. A comparison of the model predictions and the experimental results demonstrates that the numerical model was generally able to reproduce the large displacements induced by the more intense ground motion ensemble, while tending to overestimate the displacements of the less intense earthquake ensemble. This overestimation of the response was reduced through the inclusion of damping in the system. However, the addition of damping greatly increased the solve time, which is problematic for a competition, and in the case of the more intense ground motion ensemble also resulted in an underprediction of the maximum response of the structure.

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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.

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Collapse of masonry structures under the influence of seismic action typically takes place via specific failure mechanisms, which have been well-documented. Assuming these mechanisms can be modelled as a kinematic chain, equations of motion can be derived and solved to predict dynamic rocking response. Previous derivations typically assume that the kinematic chain is comprised of rigid bodies with rigid interfaces, which are assumptions that can be both unrealistic and un-conservative. In this paper, rocking equations of motion are re-derived considering the presence of flexible interfaces and crushing effects. Specifically, new derivations are presented for single, two and multiple block mechanisms, while two different formulations for modelling non-rigid interfaces are also proposed. These formulations are compared, and the importance of interface flexibility is evaluated through comparison of the new models with previous formulations that assume purely rigid interfaces. The new equations of motion are also practically evaluated through comparison with advanced numerical modelling simulations.

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The authors characterized earthen wall materials and plasters in a mid-fourteenth-century Hohokam great house at Casa Grande Ruins National Monument (Arizona) and assessed the seismic susceptibility of its puddled earth walls. Characterization included determining the microstructure, microcomposition, porosity, aggregate mineralogy, and identification of phases in the binding matrix for each of 36 samples and reconstructing plaster technologies, including material selection, preparation, and application sequences. Findings support the ideas that earthen materials were manipulated to optimize their performance to suit the unique site conditions and needs of the ancient people using the structure and included finishes that were unusual in southwestern sites from this time period. By using a new set of tools that integrate the complicated geometry of individual wall segments as captured in light detection and ranging (LiDAR) scans (models were generated in Rhino version 5) with the dynamic analysis of rocking mechanisms (tools for this analysis were developed in Rhino), seismic collapse assessment was used to identify the most vulnerable parts of the building to earthquake loading and provided an initial evaluation of the seismic overturning capacity of these wall segments.

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Out-of-plane collapse of walls is perhaps one of the most common modes of failure of masonry structures during earthquakes. Depending on the restraint conditions, walls can fail by developing a hinge along their height, thereby resulting in the formation of a two-block out-of-plane collapse mechanism. Equations of motion derived for this mechanism thus far have modelled the cracked wall as a single-degree-of-freedom (SDOF) system made up of two rigid bodies. However, most of these formulations assume that the interfaces between the blocks themselves, as well as between the blocks and the supports, are rigid. Alternatively, equations of motion have also been derived for two-block systems with flexible interfaces, which model the system as having four degrees of freedom, which is considerably more complicated than the SDOF model. Neither of these formulations account for the finite compressive strength of the interfaces, upon the exceedance of which crushing occurs, thus further reducing the dynamic resistance of the structure. This paper presents the derivation of an equation of motion for a cracked wall section taking into account the presence of flexible interfaces as well as crushing effects. Using as a case-study a typical multi-story spanning masonry wall, the importance of considering crushing during out-of-plane collapse is then quantified for a range of interface properties and loading conditions.

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Failure of masonry structures generally occurs via specific collapse mechanisms which have been well documented. Using rocking dynamics, equations of motion have been derived for a number of different failure mechanisms ranging from the simple overturning of a single block to more complicated mechanisms. However, most of the equations of motion derived thus far assume that the structures can be modelled as rigid bodies rocking on rigid interfaces with an infinite compressive strength—which is not always the case. In fact, crushing of masonry—commonly observed in larger scale constructions and vertically restrained walls—can lead to a reduction in the dynamic capacity of these structures. This paper rederives the rocking equation of motion to account for the influence of flexible interfaces, characterized by a specific interface stiffness as well as finite compressive strength. The interface now includes a continually shifting rotation point, the location of which depends not only on the material properties of the interface but also on its geometry. Expressions have thus also been derived for interfaces of different geometries, and parametric studies conducted to gauge their influence on dynamic response. The new interface formulations are also implemented within a new analytical modelling tool that provides a novel approach to the dynamic analysis of masonry collapse mechanisms. Finally, this tool is exemplified, along with the importance of the interface formulation, by evaluating the collapse of the Dharahara Tower in Kathmandu, which was almost completely destroyed during the 2015 Gorkha earthquake.

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This paper presents a new CAD-interfaced analytical tool for the nonlinear dynamic analysis of masonry collapse mechanisms. Utilizing rocking dynamics, the tool derives and solves equations of motion for a broad range of collapse mechanisms, for any user-defined structural geometry. Using as a starting point a digital drawing of the structure in Rhino (a typical CAD software), the tool computes the kinematic constants defining these equations of motion, which are then exported to MATLAB and solved for either pulse-response to generate overturning spectra, or full time-histories. The use of the tool is demonstrated by comparing its predictions to results from experimental shake-table tests, as well as against field observations from the 2015 Gorkha earthquake, while its predictive abilities are illustrated using as case-studies the Casa Grande Ruins National Monument in the United States, as well as the Church of San Leonardo Limosino in Italy, which sustained some damage during the 2012 Emilia earthquake sequence.

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This paper studies damage to a few specific monuments in the Kathmandu Valley that were either partially or completely destroyed during the 2015 Gorkha earthquake. Three of these structures—namely, the Basantapur Column, the Dharahara Tower, and the Narayan Temple—were modeled both analytically using rocking dynamics and computationally using discrete element modeling (DEM). The results emphasize the importance of large low frequency content within the ground motion, demonstrating that the Dharahara Tower could have collapsed due to the primary long-period ground motion pulse alone. In addition, comparison of analytical and computational modeling to the observed response enables evaluation of structural behavior, including discussion of the importance of elastic amplification and column embedment on performance during the earthquake.

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The 2015 Nepal Earthquake caused significant localized damage to several historic centers in the KathmanduValley. In particular, many cultural heritage structures were either partially or completely destroyed. This paper studies the destruction sustained by a fewspecific monuments in order to clarify the poor performance of certain structures in light of the unique characteristics of the ground motion recorded at the USGS KATNP station in Kathmandu. Relatively simple structures aligned in cardinal directions were selected, as these allow useful understanding of ground motion directionality. Survey data for the monuments was taken by hand and using laser-scanning, and was used to create the geometric models necessary to investigate collapse. The results explicate why these particular monuments collapsed while many structures in Kathmandu remained undamaged. In particular, the effects of the long-period shaking within the ground motion are directly considered, thereby enabling discussion as to why the distinctive characteristics of the ground motion damaged certain structures.@en

Trajan's Bridge, built by Romans over the Danube River in the first years of the II century, was the first kilometer-long bridge ever built. It was a marvel of Roman engineering, especially taking into account challenging site conditions, available resources and record time for construction. The bridge's still-standing columns are witnesses to its masterful construction. The bridge was later intentionally destroyed by Romans, and several researchers in the past studied the bridge and attempted to reconstruct its appearance and structural system. However, the dearth of information generally associated with destroyed ancient structures makes their reconstruction extremely challenging. In the case of Trajan's Bridge, the only confirmed representation of the structure is on Trajan's Column, found just north of the Roman Forum. Nevertheless, several studies performed in the past proposed a structure different from the one shown in the Column. Most of these studies are not based on detailed structural analysis, and thus some of them do not seem to be credible from the engineering point of view. The aim of this paper was to reconstruct the structural system and appearance of Trajan's Bridge using structural analysis, and to determine to what extent the representation of the structure on Trajan's Column could be accurate. This is successfully performed by determining the number of degrees of freedom associated with the structure and by analyzing the materials, stresses, and the bridge construction technique.@en

The Taj Mahal, built by the Mughal Emperor Shah Jahan to commemorate the death of his wife Mumtaz Mahal, is considered to be a marvel of Mughal construction. While the structure has been studied in great detail from an architectural perspective, limited studies have been conducted with respect to its structural stability. Furthermore, very little information exists with regard to how the building, especially its distinctive dome, was constructed. The aim of this paper was to conduct a detailed structural analysis of the dome of the Taj Mahal in order to better understand how it was constructed. This is successfully performed by conducting a finite element analysis of the structure using Abaqus CAE, and by analyzing the materials, stresses, and dome construction techniques.@en

Large displacement response of stone masonry structures often involves the opening and closing of dry joints, or hinging behaviour. Discrete element modelling (DEM) is often used to model large displacement response as it inherently captures the interaction of discrete bodies, and allows for joint contact recognition in a more efficient manner than many finite element modelling procedures. Modelling such behaviour can be computationally demanding and the problem becomes more complicated when reinforcing, often in the form of post-tensioning, is applied to prevent collapse. This paper evaluates the ability of DEM to accurately capture the behaviour of reinforced masonry as observed in an experimental study conducted at the University of Porto. The DEM software 3DEC was used to model the response of the post-tensioned arch when subjected to gravity and a superimposed dead load, and this response was evaluated for varying levels of pre-stress in the arch. A reasonably good correlation was observed between the experimental and DEM results, and the differences that do exist are discussed.

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