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Curved masonry structures externally strengthened by Fiber Reinforced Polymer (FRP) systems exhibits failure mechanisms that emphasize a local bond behavior particularly influenced by the curved geometry of the substrate and the position of the strengthening (i.e. at the intrados or extrados). Indeed, together with tangential stresses, normal stresses in tension or compression also arise by leading to a combined mode I–mode II behavior of strengthening system at the reinforcement/masonry interface level. In recent studies, the Authors proposed different modeling approaches for FRPs applied to curved masonry structures. In particular, both micro-modeling detailed approaches and simplified approaches were generally proposed. The present paper critically analyzes these models by underlining the main differences among them, the assumptions and their ability to reproduce specific phenomena experimentally observed.

New materials and techniques continuously enrich the family of fiber reinforced polymer (FRP) systems to use for retrofit interventions of existing masonry constructions. Recently, the deep mounted flexible (DMF) technique, consisting of the execution of deep grooves in the masonry where FRP strips are placed by using flexible adhesives, have been proposed. The studies available in literature show the potentialities of this technique and its advantages with respect to traditional techniques. At the same time, these studies also emphasize a behavior with specific features influencing the performance of DMF systems which need to be investigated. Aim of the present paper is to propose numerical approaches for the study of the bond behavior of DMF systems. In particular, it is presented both an approach based on the solution of the system of differential equations governing the shear stress transfer mechanism (ODE-DMF), and a simplified finite element schematization (FEM-DMF). Both the approaches are implemented in different computer codes and validated toward case studies derived from literature. The comparison with the experimental tests shows the ability of the proposed modeling approaches to reproduce the experimental response of the examined specimens by underlying features related to the shear stress transfer mechanism between the reinforcement placed in the groove and the surrounding masonry.

An extensive numerical investigation of the structural behavior of the masonry church of Sant’Agostino in Amatrice (Italy) during the 2016–2017 seismic sequence is presented. The seismic performance of the church is studied in relation to the most energetic shocks of the sequence, occurred on August 24th, 2016, and October 30th, 2016, whose seismic parameters (PGA, Trifunac duration, Arias intensity, destructiveness potential factor) are analyzed in detail. In particular, a comparison between ground motion data recorded by different stations is presented in order to evaluate the influence of local amplification effects on the structural behavior. To achieve this goal, the ground motion data recorded by the permanent accelerometric station (AMT) located in Amatrice on type B soil and belonging to the National Accelerometric Network (RAN) are firstly considered. Then, they are critically compared with those provided by an accelerometric station temporarily installed after the first main shock in the downtown area close to the church site, showing a clear amplification due to the site effects. The dynamic behavior of S. Agostino’s church is numerically investigated by carrying out a set of non-linear dynamic analyses on the 3D finite element model of the church developed in Abaqus CAE and considering as seismic input both the accelerograms recorded by the AMT fixed station and those including the local amplification effects. Non-linear properties of materials are taken into account by defining an elasto-plastic constitutive law with reasonable damage parameters in tension. Numerical results are evaluated in terms of displacement time-history of some relevant control points located on the masonry walls and maps of tensile damage cumulated at the end of the simulations. Numerical results are in good agreement with the evidence based behavior of the structure, thus validating numerical simulations as effective tools for seismic analysis of masonry buildings. Furthermore, a hypothetical strengthening intervention concerning the improvement in masonry mechanical properties is implemented in the model to investigate its positive role in preventing collapse. In the latter case, the approach provides useful hints in interpreting the behavior of the church under the application of repeated accelerograms.

Masonry has been probably one of the first structural materials used by humankind since the first centuries of civilization in a variety of applications that spans from housing to infrastructures. ...

In recent years, strengthening with Fiber Reinforced Polymers (FRPs) has emerged as an effective way for the structural upgrading of masonry elements. In such typology of external reinforcement, the bond quality is crucial for the increase of the load bearing capacity. The bond efficacy beyond the elastic limit can be studied analytically or numerically via several different models, where the most important issue to tackle is the reproduction of the typical brittle behavior of the substrate. In this paper, a simple numerical approach which models FRP as elastic and lumps all non-linearity on the FRP/masonry interface is proposed. The non-linear behavior of such interface is modeled in a simplified but effective way integrating numerically the differential equations deduced from equilibrium and compatibility (once that a non-linear constitutive relationship between tangential stress and slip is assumed at the interface). Such integration is carried out by means of a particularly simple forward scheme that requires the estimation of the slip value and its derivatives on specific knot points. A comparison against existing literature indicated that the proposed numerical procedure can adequately reproduce global load-displacement curves in standard single lap shear tests, as well predict the local slip behavior.

Externally bonded composites have become an effective alternative for building strengthening in recent years, such as FRP (Fiber Reinforced Polymer) and FRCM (Fiber Reinforced Cementitious Matrix) can be utilized in this retrofitting strategy. For masonry structure, curved members are very common and tend to be the weakest parts of the system, meanwhile exhibiting bond behavior differently from that of flat surfaces. In this article, a simplified model consisted of an elastic composite strip and inelastic brittle substrate was adopted, based on which a fully analytical approach is developed for describing the debonding mechanism of FRP/FRCM strengthened curved surface under shear force. This approach requires few parameters, and can be realized with limited computational cost in a standard MATLAB environment, while providing a stable solution. This approach was then validated against numerical method and experimental data available in literatures, proving its effectiveness and reliability.

A dynamic analysis procedure for hinge-controlled masonry arches subjected to horizontal acceleration profiles is developed. Constructed from the principle of energy conservation, the establishment...

A new procedure for a fast and comprehensive description of the collapse behavior of curved masonry structures is presented. The first step provides the identification of the exact collapse mechanism and the load-bearing capacity through adaptive NURBS limit analysis. This method is based on the discretization of the masonry vault through very few curved elements, assumed as rigid blocks with internal dissipation allowed only at interfaces, whose shape is iteratively modified until interfaces coincide with the correct position of cracks. On the obtained mechanism, a kinematic non-linear analysis with rigid-softening behavior can be also applied to better understand how the load-bearing capacity decreases during the evolution of the mechanism. A finite element (FE) non-linear static analysis is then applied to obtain the force-displacement curve according to the real elastic-softening behavior. The NURBS optimized model is converted into a discrete FE model composed of three-dimensional elastic units joint together by interfaces where the non-linear mechanical properties are lumped. Within this assumption, non-linear interfaces are applied along the cracks previously found through the limit analysis in a fully automatic way, preventing any mesh dependency effect. Furthermore, the combination of such approaches allows overcoming the respective drawbacks of the methods. Selected masonry arches and vaults are here studied to present the reliability of the presented coupled approach.

An experimental investigation aimed to analyze the mechanical behaviour of Carbon Fiber Reinforced Composite (CFRP) anchor spikes inserted in a brick substrate is reported in this paper. As is well known, such devices can improve the structural performance of CFRP sheets externally bonded to masonry elements (as well as others substrate materials). In structural applications, spike anchors can be subjected to both shear and/or normal actions; the first commonly occurs in structural applications, while the latter may occur in specific applications, such as CFRP sheets bonded to curved surfaces. For this reason, the experimental program described in this paper analyzes the mechanical behavior of a typology of anchor spikes loaded (separately) by pure shear or normal actions. Although, obviously, in anchored CFRP sheet reinforcements the contribution to the bearing capacity of the sheet and of the anchors cannot be additively superimposed (the total capacity is of course not equal to the sum of the capacity of the sheet and of the anchor), the results described in this paper can still give useful indications in practical applications.

This paper provides a comphrensive review of the critical aspects of nonlinear modeling for evaluating the seismic response of masonry structures, emphasizing the issues relevant to engineering practice. Currently, the specialized technical community shares the opinion that, for a performance-based approach, numerical models are the only tools sufficiently effective to support the seismic assessment of existing buildings. However, their potential often falls short when attempting to accurately describe the behavior of masonry structures. In fact, these structures feature highly complex architectural configurations, different masonry types, and various structural solutions, meaning that extra care is required in numerical modeling. This is especially true when the modelers do not have a solid background in the software chosen and may not be practiced using the vast variety of options offered by the software houses. They are often unaware of the consequences that questionable modeling choices may have on the results obtained by the models. These extremely complex topics are treated in the paper from an engineering practice perspective, providing an in-depth overview of the challenging issues related to the use of different modeling strategies. The paper covers strategies ranging from the Equivalent Frame approach (widelyused in common engineering practice) to more refined techniques like 2D and 3D FiniteElement procedures based on continuous, discrete, and micro-mechanical approaches. Critical aspects in the modeling of both in- and out-of-plane responses of masonry, as well as the critical issues in wall-to-wall connections and diaphragm roles are investigated. All the examined issues are clarified through numerical examples highlighting also how a consistent and integrated use of different procedures may be beneficial. Finally, some of most relevant challenging issues concerning the use of numerical models in seismic assessment with the nonlinear static approach are presented and discussed.

The aim of the paper is to extend and put at disposal to common users a reliable numerical procedure called MPM (Multi-Pier Macro) approach, already presented in-plane, for walls subjected to two way bending. This approach is developed starting from a Multi-Pier MP approach proposed by the authors in the past. The MP approach for the out-of-plane analysis of masonry can be used for practical purposes, but requires a refined discretization with relatively huge computation effort and a specific training for the user. The MPM approach overcomes some well known limitations of the MP one, using a discretization that is totally independent from the actual unit cell dimension considered and totally unrelated to the specific texture of the masonry wall considered. The MPM method relies on a very unrefined discretization of a wall out-of-plane loaded with parallelepiped cells with large edges made by vertical and horizontal beams plus braces, assuming for each element equivalent geometric and mechanical properties that guarantee the elastic, peak and post peak rough equivalence between the original masonry wall and the mono-dimensional discretization proposed. Its main feature is to allow the analysis of large and complex masonry structures, shortening the calculation time and being accessible to practitioners without a specific background on masonry and who own a commercial software equipped only with non linear 1D elements. The procedure is benchmarked on four walls out-of-plane loaded in two way bending, in presence also of perforations for three of the four walls; a good predictivity in the non-linear range is observed when compared with much more sophisticated numerical approaches.

The dynamic behaviour and the seismic vulnerability of the ancient civic tower of Amatrice, dramatically damaged by the last shocks sequence of 2016 that occurred in Central Italy, have been studied in this paper by means of advanced 3D numerical analyses with the Discrete Element Method (DEM). Thus, a discontinuous approach has been used to assess the dynamic properties and the vulnerability of the masonry structure, through large deformations regulated by the Signorini’s law, concerning the impenetrability between the rigid bodies, and by the Coulomb’s law, regarding the dry-friction model. Afterward, different values have been assigned to the friction coefficient of the models and real seismic shocks have been applied in the nonlinear analyses. The major purpose of this study is to highlight that relevant data on the real structural behaviour of historical masonry can be provided through advanced numerical analyses. The comparison between the results of the numerical simulation and the survey of the existing crack pattern of the bell tower permitted to validate the approach used. Finally, from the results and conclusions of this case study, it is possible to affirm that the used methodology can be applied to a wide variety of historical masonry structure in Europe.

This work evaluated the remarkable influence of stereotomy on discrete methods adopted for the dynamic response of an ancient masonry structure. The historic building used as a case study i...

In this work, the study of a complex masonry umbrella vault located within Masegra Castle (Museum of Sondrio territory, Northern Italy) is presented. Built during the renewal of the castle ...

The seismic response and strengthening of two complex monumental masonry churches located in Northern Italy have been investigated through an advanced macro-modelling FE-based approach. An extensive documentary research and several field surveys have provided a fundamental preliminary knowledge of the two churches. Detailed three-dimensional FE models with a damage plasticity behavior for masonry have been developed and non-linear dynamic analyses have been performed to simulate the damage distribution in the churches and to identify the most vulnerable macro-elements. The analyses have highlighted the effects of geometrical features and masonry coverings on the seismic behavior of the two churches. The examination of the results in terms of tensile damage contour plots, maximum normalized displacements and energy density dissipated by tensile damage has provided a thorough description of the seismic response of both the whole church and the different macro-elements. In this regard, the procedure utilized could be regarded as a general guideline to follow for a realistic insight into the seismic response and failure analysis of large complex masonry structures without box behavior. From the results obtained, a hypothetical strengthening intervention has been implemented in the numerical models of the two churches according to the Italian Code, in order to quantitatively estimate the vulnerability reduction. A decrease of both tensile damage and displacements has been observed for the critical elements of the two churches in the case of strengthened models. Moreover, the results have shown the importance of the presence of the nave masonry covering to increase the effectiveness of the strengthening intervention, preventing the out-of-plane mechanism of the nave walls.

In the framework of the Mediterranean cultural heritage, the term “fictile tubule” identifies a peculiar type of brick, characterized by a cylindrical shape and a hollow core. Its unique geometry and characteristics rank it among the first hollow clay bricks in history. The large-scale production of fictile tubules allegedly began in the Roman provinces of Northern Africa during the 2nd Century A.D., where they were employed for building vaulted and domed structures without the need of centrings. Over the following Centuries, the construction technique of fictile tubules embedded in mortar was constantly refined and improved. This led to an extensive use of such technique in several buildings - as part of different structural elements (vaults, domes, floors, walls) - all over the Mediterranean area, and especially in Southern Italy. In 1909, after the disastrous earthquake in Messina and Reggio Calabria, Calabrian engineer Pasquale Frezza devised and patented an anti-seismic construction system which evolved the technology of casa baraccata. Frezza’s take on this traditional Calabrian way of erecting buildings involved the use of a specific type of fictile tubule, named carosello, alternated with common bricks in masonry walls, which are then encased in a timber frame. This paper presents an investigation on the structural behavior of Frezza’s evolution of casa baraccata, aimed at its possible revival as a relevant anti-seismic construction technique. Two specimen walls with dimensions equal to 60×60×15 cm3 are built according to Frezza’s patent and experimentally examined through a diagonal compressive test at the Civil Engineering Laboratory of University of Calabria. For the first specimen wall the test is carried out until failure to identify the collapse load. Conversely, for the second specimen wall the test is halted immediately after the formation of the first vertical cracks. The specimen is subsequently repaired using B-FRCM (Basalt Fiber-Reinforced Cementitious Matrix) as reinforcement, and the diagonal compressive test is repeated, this time until failure. The results in terms of collapse load and shear strength for both specimens are then compared and critically discussed, highlighting the increased load-bearing capacity of the wall built according to Frezza’s patent and reinforced with B-FRCM.

The main results of an experimental program concerning masonry pillars reinforced by CFRP strips (also provided by spike anchors) subjected to single lap shear tests are described in this paper. The experimental results, also compared with a previous experimental program, allowed to analyze the increment of bearing capacity produced by spike anchors to CFRP sheets having different bonding length.

The studies contained in the current literature particularly emphasize the importance of the role of the local bond mechanism on the global performance of fiber reinforced polymer systems (FRPs) employed for the strengthening and the rehabilitation of structures. Nevertheless, although several applications of FRPs involve curved masonry structures (arches, vaults, domes, etc.), the bond mechanism of FRPs applied on masonry samples with curved substrates is a topic still scarcely investigated and the actual guidelines do not provide specific design formulas. The aim of the present paper is to analyze the main features characterizing the bond behavior of FRPs externally applied to masonry specimens with a curved substrate configuration throughout a simple modeling approach based on the interface concept. Particular consideration is devoted to the development of suitable constitutive laws for the FRP/masonry interface. Considering case studies derived from the current literature, consisting of shear-lap bond tests of curved masonry specimens characterized by different curvatures of the bonded surface and different strengthening configurations, numerical analyses are carried out in order to emphasize the ability of the model to capture the bond behavior of FRP applied on curved masonry substrates.

Aim of the present paper is the proposal of a simple modeling approach for the numerical simulation of the bond behavior of masonry specimens externally strengthened by FRP strips equipped with anchor spikes. The model is based on a simple 1D-schematization of specimens, previously proposed by the authors and based on the use of linear and nonlinear spring elements schematizing the support, the FRP, the masonry/FRP interface. The approach here proposed specifically considers the coupled behavior between shear and normal stresses arising at the masonry/FRP interface level and, moreover, it introduces constitutive laws for modeling local failure mechanisms involving the anchor. The parameter setting procedure presented in the paper is indeed devoted to implicitly consider the contribution of the anchor and its interaction with the masonry support, directly at the FRP/masonry interface level. This allows to reduce computational efforts while preserving a good reliability level of the model. The validation of the proposed modeling approach is here carried out by considering experimental tests performed by the authors and available in the current literature. The results obtained from the numerical analyses reported in the paper show both the reliability of the proposed approach to capture the experimental behavior and, moreover, its efficacy for investigating the role of the anchor on the bond behavior of the strengthening system.

This paper presents a novel and straightforward procedure for the derivation of homogenized failure surfaces for non-periodic masonry. The most innovative feature of this procedure is the automatic generation of a convenient finite element mesh directly from the sketch of the considered masonry panel, based on the so-called “pixel strategy” that converts each pixel into an element. An upper bound limit analysis problem coupled with homogenization is then solved by aptly formulating it as a linear programming problem. Another main feature is the implementation of a reduced formulation of such problem (called “master-slave approach”) so that the number of unknown variables is reduced and, consequently, the computational times needed for the extraction of the homogenized failure surfaces are shortened as well. A simple procedure is also implemented for a quick identification of the statistical Representative Element of Volume (or REV) for a non-periodic masonry panel. The REV is the smallest portion of a composite material that includes all the physical and geometrical characteristics needed for its complete description. The reliability of the procedure is tested by investigating six case studies displaying different degrees of non-periodicity, extracting and critically commenting the results obtained in terms of homogenized failure surfaces and failure modes.

The historical centres of many Italian cities are integral parts of the Country’s cultural heritage, and guaranteeing their conservation over time is paramount. Many constructions are characterised by building techniques that are not well-known and still have to be studied. In particular, one technique involving the use of clay fictile tubules is here examined through historical studies, experimental characterisation and numerical investigations. This technique is typical of the Mediterranean area and Southern Italy, and dates back to Roman and early Christian times; three different types of elements were usually employed (tubules, amphorae and caroselli). Walls, domes and vaulted structures with different geometries were built with this technique, which allowed for the creation of modular construction elements in potteries. Relevant historical building issues are first addressed in detail, then a comprehensive experimental investigation on the constitutive materials (caroselli and mortar) is presented, provided with a series of numerical simulations aimed at validating the experimental results. Eventually, the composite material consisting of caroselli and mortar is investigated through a homogenisation approach, allowing its mechanical characterisation through the evaluation of equivalent homogenised material properties. They are derived through the investigation of an analytical elementary cell, subject to uniaxial tension and compression, which enables to derive homogenised constitutive laws. These are validated by comparing experimental data obtained from compressive tests performed on three real elementary cells with numerical results gathered from the use of such homogenised properties on an equivalent cell.

The seismic performance assessment of historical masonry structures is still a complex issue in civil engineering. This paper investigates the seismic response of seven masonry churches, which are located in the province of Ferrara (Northern Italy) and suffered extensive damage during the 2012 Emilia earthquake. Different field surveys, which were conducted after the earthquake to collect information on typical damage patterns, provided a preliminary knowledge of utmost importance for developing detailed FE models of the churches and for better understanding the results of advanced numerical simulations. First, modal analyses were performed to have a preliminary insight into the dynamic behavior of the churches. Then, non-linear dynamic analyses with different peak ground accelerations were carried out in order to obtain the damage distribution in the churches and to identify the most vulnerable macro-elements. The results highlighted the influence of morphological and geometrical characteristics on the seismic behavior of the different macro-elements composing the churches.

Reinforced Concrete (RC) buildings with masonry infills are a very common structural typology worldwide for civil, strategic, or productive use. Damage to infills may cause danger for human lives and strongly affects economic losses, as shown during past earthquakes. In the current literature, different approaches are available for modeling the in-plane response of infilled frames and different constitutive laws generally calibrated on experimental tests. On the contrary, few and recent studies proposed formulas that account for the main properties of infills influencing their in-plane behavior to lateral forces. This paper presents a study finalized to derive a reliable model that is able to predict the monotonic and cyclic response of RC infilled masonry frames. To this end, after a critical analysis of the available literature, the authors combine among them two models, one for the monotonic response and the other for the cyclic one, by showing their reliability with reference to different experimental cases. Then, at the end of the paper, the derived models are employed to assess the seismic vulnerability of infills throughout a proposed procedure based on the common pushover analysis approach.

Partially grouted reinforced masonry (PG-RM) shear walls have been widely used as structural elements in low- and medium-rise earthquake-resistant buildings. Nonetheless, assessing its shear strength represents a complex task mainly because the partial grouting provides a non-constant cross section, which results in heterogeneous stress–strain patterns. Consequently, refined modeling techniques are needed to reproduce local failure mechanisms taking place in these walls, which significantly influence the global response. In response to this issue, a detailed micro-modeling approach based on the finite element method was proposed in previous studies by the authors. Although the numerical strategy provided accurate results, further validation is required. Therefore, in this study, the experimental results of seven PG-RM shear walls of multi-perforated clay bricks with bed-joint reinforcement are employed as validation cases. These seven walls presented variations in five design parameters. The validated numerical model was then employed to perform a parametric study to assess the influence of the wall aspect ratio, axial pre-compression stress, and horizontal reinforcement ratio on the in-plane lateral behavior of PG-RM shear walls. The obtained results show that the three studied design parameters modified the crack patterns of the walls. Besides, increasing the axial pre-compression stress or reducing the aspect ratio resulted in higher walls’ shear strength. Additionally, decreasing the horizontal reinforcement ratio or increasing the aspect ratio generated a higher story-drift ratio at maximum lateral force. Finally, it was corroborated that the positive effect of the axial pre-compression stress on the walls’ shear strength decreases inversely proportional to the aspect ratio.

The paper chose Longhu pagoda (built in 1342 A.D.) which is the only Yuan dynasty masonry pagoda in Si-chuan province of China as case study. According to the previous numerical research in the field and post-earthquake surveys experience, assume for masonry a Concrete Damage Plasticity CDP material model, pushover analyses and non-linear dynamic analyses were carried out by Abaqus software. The aim is to predict the state, characteristics and distribution of damage of the structure in an accurate way, and analysis the vulnerability of the masonry pagoda.

The current paper aims at analysing the effect of ground motion vertical component in the case of near-field excitations on the structural response of historical masonry buildings. In this perspective, the Banloc Castle in Romania has been considered as a reference case study. This historical masonry structure was damaged by the Banat-Voiteg earthquake that occurred in December 1991 in the homonymous city. To this purpose, a FEM model of the building, set up using the DIANA FEA analysis software, has been studied in the non-linear dynamic field considering a real ground motion record based on specific source-to-site distance, moment magnitude and focal depth. The effects of the impulsive earthquake have been evaluated considering the main engineering demand parameters, such as displacements and forces, focusing on two different scenarios, namely horizontal and horizontal + vertical ground motions. The obtained results have shown that the vertical ground motion sensibly modifies the structural capacity of the building since it produces a relevant modification of the in-plane walls behaviour and the stress conditions. Important considerations about the behaviour (or seismic response modification) factor, ductility and stress in terms of axial and shear forces have been provided. Moreover, numerical damage patterns have been compared to the real cracks detected. Finally, a set of fragility curves has been derived taking into consideration the near-field effects., (undefined)

Thousands of rural houses in developing countries with high seismicity were built without adequate seismic protection due to economical reason. This paper discusses a possibility to improve the seismic protection of typical unreinforced masonry in developing regions using low cost base isolation devices. The proposed isolation system involves fibre reinforced elastomeric isolators (FREIs) having small dimensions and few layers of rubber pads to reduce the fabrication cost. A series of 3D FE simulations are carried out to investigate the performances of the proposed FREIs utilised in the isolation of a one story masonry house prototype. The model is assumed subjected to several accelerograms to have an insight into the sensitivity of the isolation system against different earthquakes. The results reveal that the proposed low cost FREI system provides significant damage mitigation to the masonry house with good applicability of the FREI devices.

The main aim of using the IoT paradigm is related to the possibility of a connectivity extension of several common SHM devices by means of Internet. The connected devices are thus able to transmit and process data, guaranteeing new scenarios in the design of acquisition systems in different fields of science and engineering. The innovations have led the researchers to extend the application of the IoT paradigm to the SHM of masonry structures making sure that the experiments conducted in this framework are able to ensure good results with promising future improvements. The main uses, to date, have been implemented, for example, to monitor individual structural elements, reducing the risks for users due to partial or total collapses of the structure, or for the identification, detection and characterization of damage and degradation of construction materials. The aim of this work is to expose a general overview of the SHM systems used by the authors for masonry structures belonging to historical and cultural heritage, arguing their use for the protection from earthquakes with related advantages. This will be shown thanks to two preliminary SHM systems designed and implemented by the authors on two case studies using IoT, described in the paper with their related cyber and physical parts.

Retrofitting of arches, vaults and domes is needed for vulnerability mitigation of historical structures. Lately, the external application of composite materials embedded within an inorganic matrix addressed the compatibility issues related to FRP applications. Great efforts have been made for a correct identification of tensile and bond properties of TRM reinforcement, but scarce data are available for understanding the effect of curvature in debonding. This paper provides a numerical approach that enables to predict the reinforcement performance on curved masonry elements, when the same is designed without having specific single lap shear tests for the adopted materials. Such an approach relies on a separate modeling of each constituent material of the reinforcement and the substrate: matrix, fibers and the interface between them, and bricks and mortar joints. The FE-based software Abaqus is used for the simulations, addressing the non-linear material properties by means of the CDP constitutive model. In order to calibrate and validate the proposed numerical approach, experimental data are used and through a comparison of the load–displacement curves obtained the capabilities of the method are discussed. Finally, an extension of such approach to curvatures not experimentally tested is presented, opening the way to future applications of the approach., (undefined)

A fast two-step procedure for the numerical analysis of curved masonry elements is here proposed. The approach relies on a preliminary kinematic limit analysis by means of consolidated NURBS and mesh adaptation, followed by a non-linear analysis carried out with a discrete model coupled with homogenization procedures. Such an approach allows identifying at first the mechanism of collapse for an assigned load. Then the configuration at the collapse is taken into account in the preparation of the discrete model. The discrete model results as an assembly of elastic units joint by non-linear interfaces. These latter ones are modeled with 3D linear brick elements and Concrete Damage Plasticity (CDP), available in Abaqus, is used for modeling the non-linear mechanical properties coming from the homogenization step. The novel discrete approach is validated taking advantage of numerical data already available in literature treating a masonry cloister vault subjected to a vertical incremental load. Afterward, the two-step approach is applied to the same geometry but imposing an inclined force at the top. The combination of such approaches allows overcoming the respective drawbacks of the methods. A numerical comparison in terms of damage pattern and curve load-displacement is finally provided.

The aim of this paper is to present the development of discontinuous approaches to simulate the nonlinear dynamic behaviour of the civic clock tower of Rotella, in the province of Ascoli Piceno (Italy). The study involves the use of the Non-Smooth Contact Dynamics method implemented in the LMGC90© code, where sliding motions are governed by Signorini's impenetrability condition and dry-friction Coulomb's law, and the Discrete Element Method with cohesive and tensional behaviours at the joints in the 3DEC© code. The tower was represented using three different geometric models ranged from the most complex one, including the full geometry and multi-leaf masonry walls, to the simplest one, including the single-leaf walls as a simplification of the real masonry. The numerical results highlighted the modes of failure depending on the shape, size and texture of the masonry and the modalities of progressive damage under dynamic actions. Moreover, both numerical approaches have proven to be capable of simulating large displacements and complete block separations, reproducing complex mechanical behaviours and making predictions on the vulnerability assessment of the historical masonry buildings.

In this work, a simple and effective Rigid Beam Model recently introduced for studying the dynamic behaviour of ancient freestanding stone columns is extended to the case of cantilever unreinforced masonry walls, considered along their thickness and subjected to out-of-plane loading. Both monolithic and multi-block walls were investigated. The proposed model assumes each block of the wall as a rigid beam element and each interface as a node. By assuming no sliding along the interfaces and small displacements of blocks, rocking can be simulated by a bi or tri-linear moment rotation non-linear constitutive law. Different in geometry monolithic and multi-block masonry walls were developed in the numerical model and subjected to different in magnitude and frequency harmonic loading. Their response was compared against those from the literature and good agreement was found. From the analysis results, it was found that monolithic walls can overturn with acceleration magnitudes larger than their corresponding static load multipliers, if input frequency values increase. However, overturning accelerations of multi-block walls increase less rapidly for increasing input frequency with respect to the corresponding equivalent monolithic walls. Collapse mechanisms involving wall portions above the base were found in addition to traditional overturning ones with respect to the base. To ensure reproducibility of results, input and output files will be made publicly available.

As an important historical building type for human beings, ancient masonry pagodas have key research significance. They are widely diffused in China, and they are tower-like masonry structures, usually massive and tall. This paper takes the Longhu pagoda as a case-study: it was built in 1342 CE, and it is the only masonry pagoda from the Yuan Dynasty. It is located in the Sichuan Province (China), it has a square plane, and the height is about 33 m. This construction severely suffered the so-called “2008 Sichuan Earthquake”. A full 3D model of the Longhu Pagoda has been obtained and subsequently meshed. The FE software Abaqus/CAE has been used for carrying out static analyses, pushover analyses and non-linear dynamic analyses. The material non-linearities have been taken into consideration employing the so-called Concrete Damage Plasticity (CDP) model available in Abaqus. Modal analyses have shown that FEM results and simplified cantilever model results may agree. Pushover analyses (POs) have been performed under different load conditions and along the four principal bending directions to estimate the global capacities and the corresponding collapse mechanisms. Non-linear dynamic analyses (NLDAs) allowed putting in evidence the accuracy of the results provided by the pushover analyses; besides, they gave helpful information about the crack propagation, confirming the damage reported on-site after the 2008 earthquake. The state of damage found and the related failure mechanisms have been deeply commented. Moreover, some sensitivity analyses have been performed to study the influence of some material parameters on the pushover results. Furthermore, two fictitious 3D models of the pagoda have been created by doubling and removing two floors to investigate the influence of the tower slenderness. The before mentioned analyses have also been performed on such models, and the impact of the slenderness on this structural typology has been studied. Finally, the kinematic theorem of limit analysis has been applied, and some values of collapse acceleration have been consequently computed using different a-priori established collapse mechanisms. The results have been compared with FE simulations results, and the ability of limit analysis to quickly predict the seismic vulnerability has been discussed.

We present here an improvement in the non-uniform rational Bezier spline (NURBS)-based kinematic limit analysis approach, which has proven to be particularly effective for masonry vaults, by adding an innovative mesh adaptation scheme. The procedure is based on the application of the kinematic theorem of limit analysis on a 3D model composed of NURBS rigid blocks. The definition of curved geometries through NURBS surfaces allows using mesh of few elements without modifications of the real geometry. An adjustment of the initial mesh is needed to minimize the kinematic load multiplier. Therefore, a Prey-Predator Algorithm (PPA), an innovative meta-heuristic algorithm based on the natural interaction between a predator and preys, is implemented as core of the mesh adaptation, allowing an efficient evaluation of load-bearing capacity and collapse behavior of masonry vaults. In this work, the standard PPA is further improved by introducing a variable population size, the so-called saw-tooth model, which allows reducing the computational effort without penalizing the evaluation of the objective function. Some numerical examples, which involve a masonry arch, a skew arch, and a horizontally loaded dome, are finally analyzed. For all the cases, a comparison between the proposed PPA and a traditional Genetic Algorithm (GA) is presented.

The vibration response of a full-scale polycentric near parabolic tuff barrel vault under differential settlements of the abutments are experimentally analyzed. During the experimental tests, the static and dynamic responses of the vault have been continuously monitored through a large number of sensors of different kinds placed in suitable points of the structure and supports. The data acquired by the accelerometric sensors are used for detection, localization, and quantitative assessment of the damage by means of a dynamic damage identification (DDI) procedure specifically developed for arches. Numerical models calibrated from experimental results are employed to evaluate the effectiveness of the proposed DDI approach. The position of the crack hinges related to the experimental and theoretical collapse mechanism of the vault, along with their actual depth, turn out to be effectively identified through the proposed DDI procedure, showing the capabilities of such an approach for assessing damage even in existing full-scale masonry constructions.

This work presents an investigation on the in-plane behavior of a masonry wall that is subjected to a ground settlement in its bottom-right corner. Three distinct modeling strategies are here employed: the first two are the traditional heterogeneous and homogeneous approaches, the third a novel Genetic Algorithm adaptive homogeneous approaches. The traditional heterogeneous approach adopts a discretization of the masonry wall in which each brick is modeled as a single element. The traditional homogenous approach instead adopts a mesh consisting of triangular elements, which are considered as rigid blocks. For this latter case, the failure surfaces of the interfaces are obtained through a homogenization procedure. Eventually, the GA-adaptive homogeneous approach adopts a mesh consisting of a limited number of rectangular elements; subsequently, the initial mesh is iteratively modified to identify automatically the actual position of the cracks originated from the application of the settlement. It is also shown that the GA-adaptive homogeneous approach requires a reduced computational effort with respect to the traditional techniques.

Retrofitting of curved masonry elements as arches, vaults and domes is often a key aspect in a process of vulnerability mitigation of historical structures. Lately, the external application of composite materials embedded within inorganic matrix has met the requirements suggested by ISCARSAH guidelines. In literature, great efforts have been addressed for a correct identification of tensile strength and ideal bond length of TRM reinforcement. On the other hand, few data are available for a deep understanding of the effect of the curvature on the bond properties. This paper aims to provide a numerical tool enable to predict such a fundamental aspect when a reinforcement on curved masonry elements is designed. Experimental data are used and through comparison of curves load-displacement, the capabilities of the method are shown.

The aim of this work is to present a simple and practical experimental technique for the estimation of the ultimate shear capacity of perforated in-plane loaded dry joint masonry panels. The test is carried out by using a tilting table; in-scale models of several different perforated walls are assembled and positioned on the tilting table. The table is progressively tilted in quasi-static conditions, in order to reproduce the action of a static horizontal load proportional to masses. As a result, the model collapses for a given tilting angle, which represents the ultimate destabilizing horizontal action. The experimental setup was applied to a series of seven different masonry panels, conceived by different University teams from different countries in the context of a student competition proposed in the occasion of the 10th international Masonry Conference (10th IMC), held at the Technical University of Milan from 9th to 11th July 2018. The aim was to design a running bond shear panel with established height over length ratio, a minimum perforation ratio equal to 30% of the area and clay bricks with given dimensions disposed in either stack or running bond. The winning team was that obtaining the largest inclination angle of the tilting plane activating the collapse of the structure. Three replicates of the same experimental test were repeated in the lab of the Technical University of Milan to reduce experimental scatter of the results. In this paper we present and discuss the outcome of the experimentations carried out, in view of analyzing such results with sophisticated limit analysis approaches in the second part of the paper. The test requires simple and inexpensive instrumentation and can be adopted for a reliable prediction of the behavior of perforated shear walls in-plane loaded, assembled with dry joint bricks and horizontally loaded.

This work extends the validation of a detailed micro-modeling approach for simulating the in-plane shear behavior of partially-grouted reinforced masonry shear walls with bed-joint reinforcement. Seven walls are reproduced and used as study cases. They presented variations on the (i) aspect ratio, (ii) bricks’ height, (iii) joints’ thickness, (iv) axial pre-compression, and (v) horizontal reinforcement ratio. The results indicated that the modeling approach is suitable for reproducing the lateral resistance of this type of wall and its failure mode. Although predicted deformation capacities presented higher deviation from experimental results.

In this paper, the three-dimensional analysis of masonry vaults subjected to differential settlements is presented. A representation through NURBS shell elements is followed. Elements are idealized as rigid blocks and jumps of displacement can occur only at interfaces. Starting from a known displacement at the external boundary, the overall displacement field is determined through standard linear programming formulations. A mesh adaptation governed by a Genetic Algorithm is then applied to find the shape of the mechanism deriving from the settlement. The procedure is here applied on a historical barrel vault and results are compared with previous experimental tests.

The paper presents some SHM results belonging to a wide experimental campaign conducted on a multi-arch masonry bridge located near Mumbai (India), exhibiting a large longitudinal crack on one of the arches and the corresponding advanced numerical evaluations carried out with a NURBS kinematic limit analysis approach, used to assess the stability of the arch subjected to the passage of heavy traffic loads. The masonry bridge is a three-arch structure built during the mid-19th century by British engineers to connect Bombay with the inland of the Indian subcontinent. At present, it is characterized by a heavy state of degradation especially in one of the arches that requires an immediate evaluation of the safety under the passage of traffic loads and possible ideas of interventions to strengthen the structure, in order to avoid the propagation of deep cracks along the longitudinal direction. The adopted SHM includes the crack growth monitoring and tilting of the spandrels under the application of two different heavy loads (a water tank truck and a hydra crane) located in different positions of the arch. Numerical modelling is carried out with a full 3D approach with NURBS finite elements in limit analysis that takes into account the pre-existing crack opening and predicts with great accuracy the ultimate loads in different scenarios and the corresponding active failure mechanisms. From experimental monitoring and numerical simulations results, it is concluded that the bridge is still safe under the passage of traffic loads, but approaches the ultimate limit state for some specific configurations of the loads applied. A refurbishment is therefore needed to avoid any further propagation of the cracks up to collapse.