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Historic masonry buildings often require structural repair or retrofit to attain a satisfactory level of seismic resistance. This paper analyses the effect of externally bonded fibre-reinforced polymer (FRP) retrofitting systems on the global seismic response of such buildings in order to achieve the fundamental code-based requirements that refer to the structure’s state of damage for a specified limit state. As a case study, a three-storey historic unreinforced masonry (URM) building was selected. The first part of the paper presents an FRP design procedure for determining which vertical structural elements should be retrofitted and to what extent. As a result, six different FRP retrofitting layouts have been selected and analysed with the aid of non-linear static analyses in the second part of the paper. The paper concludes with a cost-feasibility study by introducing a cost-effectiveness index for FRP reinforcement that identifies the effectiveness of an FRP layout by accounting for the amount of retrofitting material used and comparing it with its effectiveness in improving the global seismic resistance.

To date, several different structural representations of masonry are available for use in the numerical and analytical assessment methods, each calling for a distinct level of refinement regarding the material input. To determine material properties, in terms of strength, stiffness, and toughness under compression, bending, and shear loading, extensive experimental research is necessary. To minimise the burden associated with performing complex and invasive experimental studies, this paper investigated the possible correlations between different material properties, particularly toughness, which received limited attention in past research. The correlation study was mainly conducted on the rich database established from tests on laboratory-made as well as specimens extracted from unreinforced masonry structures built between 1910 and 2010 in the Netherlands. Considering the outcomes of the correlation study, this paper puts forward recommendations to indirectly derive elastic and toughness properties as a function of strength properties. In this way, a complete picture of material properties can be obtained, while minimising the number of experiments and the extent of their invasiveness.

The Extended Limit Analysis of Reinforced Masonry (ELARM) is a simple and user-friendly method for the design and structural analysis of singly-curved, reinforced tile vaults [1]. It is based on limit analysis but takes into account the reinforcement’s contribution to the composite cross-section’s bending capacity. A three-dimensional approach to ELARM is presented in this paper. The theoretical framework to understand the implications and limitations of extending ELARM to fully 3D structures is described, together with the strategies to carry out the leap from 2D to 3D. This extension is a lower-bound approach for the design of reinforced masonry, reinforced concrete and concrete-masonry composite shells and the assessment of their strength and stability against external loading. The new, extended method is implemented computationally to speed up the iterative processes, provide quick structural feedback, offer immediate results and allow for user-interactive form-finding and optimisation procedures. Different applications of the developed tool are described through the presentation of examples, including reinforcement optimisation, a form-finding process and a case with a shape beyond funicular geometry. [1] D. López López, P. Roca, A. Liew, T. Van Mele, P. Block Tile vaults as integrated formwork for reinforced concrete: Construction, experimental testing and a method for the design and analysis of two-dimensional structures Eng Struct, 188 (2019), pp. 233-248, 10.1016/j.engstruct.2019.03.034, Structures, 35, ISSN:2352-0124

One way to improve a structure’s total load-bearing capacity during an earthquake is to apply fiber-reinforced polymers (FRP) to unreinforced walls. The study discusses the use of FRP to strengthen unreinforced masonry (URM) structures. Although, many studies were conducted on the FRP strengthening of URM buildings, most of them were experiments to investigate the success of retrofitting approaches, rather than developing a successful design model. A database of 120 FRP-reinforced wall samples was created based on the current literature. Various approaches for calculating the bearing capacity of FRP-reinforced masonry are presented and detailed. The findings of the experiments, which were compiled into a database, were compared to those derived using formulas from the literature and/or building codes, and the model’s limitations are discussed.

This study presents the results of an experimental and numerical program carried out on unreinforced masonry panels strengthened by textile-reinforced mortar (TRM) plastering. For this purpose, five panels were constructed, instrumented and tested in diagonal shear mode. Two panels were tested as reference. The first reference panel was left unstrengthened, while the second one was strengthened by a traditional self-supporting cement mortar matrix reinforced with steel meshes. The remaining three panels were strengthened by TRM plastering applied on one or both faces and connected with transversal composite anchors. The numerical and the experimental results evidenced a good effectiveness of the TRM systems, especially when applied on both panel facings.

This paper presents a study on the in-plane shear response of partially-grouted reinforced masonry walls with bond-beam reinforcement. A database of 95 tests on partially-grouted walls made of concrete hollow blocks was compiled from experimental studies reported in the literature to characterize the capacity and damageability of walls subjected to in-plane lateral loading. The database has been used to evaluate the accuracy of existing design shear strength equations for partially-grouted walls. It is concluded that the shear strength expressions in the Masonry Standards Joint Committee (MSJC) code and Canadian standard are unconservative for partially-grouted walls. A modified equation based on the MSJC expression is proposed which better estimates the shear strength of this type of walls. Seismic fragility functions are also derived based on the experimental database to calculate the probability of experiencing moderate and severe damage in a partially-grouted wall for a given story-drift ratio deformation or normalized shear force demand. The resulting fragility functions show that the normalized shear demand is better correlated with the level of damage than the story-drift ratio. The first author Z. Zhang gratefully acknowledges the financial support provided by a Harbin Institute of Technology scholarship to conduct research as a visiting scholar at the University of Texas at Austin under the supervision of the second author J. Murcia-Delso. The co-authors C. Sandoval and G. Araya-Letelier are grateful for the funding provided by the Fondo de Fomento al Desarrollo Científico y Tecnológico (FONDEF) under Grant N° 17I10264 and the Fondo Nacional de Ciencia y Tecnología de Chile (FONDECYT Regular) through Grant No. 1181598.

The retrofit solutions studied herein aim to improve the seismic and energetic behaviours of existing masonry buildings to guarantee safety and the preservation of the building heritage. The retrofit consists of timber-based products (panels and strong-backs) fixed to the masonry walls using mechanical point-to-point connections, the durability and the hygrothermal performance of the solutions are guaranteed by insulation layers and membranes. The thermophysical properties of the retrofitted walls were evaluated by means of analytical and numerical analyses, considering the heat transmission in both steady and unsteady state conditions and the thermal bridge in correspondence with the corner of the wall. The in-plane seismic behaviour of the retrofitted walls was numerically investigated through nonlinear analyses. The influence of various parameters (such as masonry and insulation properties) on the performance of the retrofit solutions was analysed via parametric simulations.

Prefabrication has been shown to be an effective way of construction in the modern-day context. Although much progress has been made in developing reinforced concrete (RC), timber and steel prefabricated elements/structures, prefabrication of masonry walling systems has received limited attention in the past. Conventional masonry construction is labour-intensive and time-consuming, therefore, prefabrication can be an effective solution to accelerate the masonry construction to make it more cost-effective. Therefore, in this paper, an attempt has been made to evaluate the effectiveness of prefabricated masonry systems (PMS) in terms of their structural characteristics and sustainability perspectives in an Australian context. Subsequently, the available studies related to PMS and the prospects of developing prefabricated masonry walling systems were appraised and reported. In order to assess the applicability of PMS, a case study was carried out by designing four types of prospective prefabricated masonry walling systems for a typical housing unit in Australia. It was shown that the reinforced (RM), post-tensioned (PT) and thin layered mortared (TLM) masonry systems are better suited for prefabrication. Later, in order to assess the sustainability of the considered masonry walling systems, life cycle energy analyses were carried using the Environmental Performance in Construction (EPIC) database. It was found that there can be nearly 30% and 15% savings, respectively, in terms of energy saving and CO2 emissions in prefabricated construction than the conventional masonry construction. Finally, the prospects of developing PMS and the need for future research studies on these systems are highlighted.

An experimental programme was carried out on long-span masonry walls made of hollow concrete blocks. Both low-rise unreinforced walls and tall reinforced walls were subjected to four-point bending tests. The tests aim at obtaining indications on the flexural capacity of partially grouted, long-span masonry walls, which basically consist of unreinforced walls laterally supported by reinforced columns, and are mainly subjected to transverse loads. The tests on reinforced walls were also intended to compare the effectiveness of two types of reinforcement (a traditional one and an innovative one in which stirrups are replaced by metal strips welded to the longitudinal rebars) on the flexural capacity. Eurocode 6 is found to strongly underestimate the experimental flexural strength of the unreinforced walls. The traditional reinforcement was found to be more effective than the innovative one. Eventually, a finite element model of the reinforced walls was developed to try and capture their failure modes. Upon a careful calibration, the numerical model is able to match the experimental ultimate load, although the real transverse displacements cannot be correctly captured.

Made available in DSpace on 2019-10-03T17:31:46Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-08-01. Added 1 bitstream(s) on 2019-10-04T16:20:51Z : No. of bitstreams: 1 S1983-41952019000400884.pdf: 2851790 bytes, checksum: ebaa6507d00b6e0104e34d8fb682dfdf (MD5) Resumo Vigas são submetidas à flexão e cisalhamento, sendo esse último esforço o tema desta pesquisa. O objetivo deste trabalho é analisar especificações para dimensionamento ao esforço cortante de vigas de alvenaria estrutural em blocos de concreto, a partir de extensa avaliação da literatura e de ensaios experimentais aqui relatados. A partir desse escopo, são sugeridas especificações para revisão da normalização brasileira. Na parte teórica, foram considerados trabalhos anteriores tanto nacionais quanto internacionais e as prescrições das normas brasileiras NBR15691-1/2011 e NBR 6118/2014, além da norte-americana, australiana, canadense e europeia, TMS 402/2016, AS3700/2001, CSA S304/2014 e EuroCode 6.1/2001, respectivamente. Com intuito de analisar e validar as especificações da literatura foi realizado um programa experimental de análise de dez vigas de alvenaria com blocos de concreto submetidos principalmente ao esforço cortante. Foram consideradas vigas de duas fiadas, três posições da carga vertical, variando a/d, e duas taxas de armadura transversal. Na análise dos ensaios verificaram-se semelhanças no comportamento último das vigas de alvenaria armada com a teoria proveniente das vigas de concreto armado, com algumas particularidades de fissuração na região das juntas de argamassa. Além disso, as especificações estabelecidas pela norma brasileira e europeia levaram a resultados consideravelmente maiores do que os resultados experimentais, enquanto que os presentes nas normas TMS 402/2016, AS3700/2001, CSA S304/2014 e NBR6118/2014 levam a resultados próximos aos obtidos experimentalmente. Como conclusão pode-se destacar que o padrão de ruptura é semelhante ao esperado para vigas de concreto armado, as fissuras foram condicionadas pela posição do ponto de aplicação do carregamento e pelas juntas de argamassa, o aumento da taxa de armadura transversal levou ao aumento da força cortante de ruptura. Os resultados indicam não ser consistente a consideração de aumento aparente da resistência ao cisalhamento pela relação M ⁄ (V∙d). Eliminando-se essa recomendação, considerando a resistência da alvenaria igual a 0,35 Mpa, limitando a tensão nos estribos a 0,90 de fyk e considerando a contribuição da armadura longitudinal, foi possível estimar o valor de cortante na ruptura de cada viga entre 73% a 106% dos valores verificados nos ensaios. Abstract Beams are subject a flexure and shear, with the last as the theme of this research. The purpose of this paper is to analyze specifications for the shear design of concrete block structural masonry beams, based on an extensive literature review and experimental tests here reported. From this scope, specifications for revision of Brazilian standardization are suggested. In the theoretical part, literature review from both national and international researchers were considered and the specifications of Brazilian standards, in addition to North American, Australian, Canadian and European, ABNT NBR 15961-1/2011, ABNT NBR 6118/2014TMS 402/2016, AS3700/2001, CSA S304/2014 and EuroCode6.1/2001, respectively. To analyze and validate the specifications of the literature, an experimental program was carried out assessing ten concrete block masonry beams results tested mainly to shear loads. Two-course high beams with three vertical load positions (position a/d) and two transverse reinforcement rates were tested. The specifications from the Brazilian and European standards led to considerably higher results than the experimental results, while those presented in the standards TMS 402/2016, AS3700/2001, CSA S304/2014 and NBR6118/2014 lead to results close to those obtained experimentally. As a conclusion, it can be noted that the rupture pattern is similar to that expected for reinforced concrete beams, the cracks were conditioned by the position of the loading point and by the mortar joints positions, the increase in the transverse reinforcement ratio led to an increase in the shear force. Results indicate that the consideration of apparent increase in shear strength by the ratio M ⁄ (V∙d) is not consistent. Eliminating this recommendation, considering the masonry shear strength equal to 0.35 MPa, limiting the stirrups tension to 0.90 of fyk and considering the contribution of the longitudinal reinforcement, it was possible to estimate the shear value at the rupture of each beam between 73% to 106% of the values verified in the tests. Universidade Federal de São Carlos Departamento de Engenharia Civil Universidade Estadual Paulista Departamento de Engenharia Civil Universidade Estadual Paulista Departamento de Engenharia Civil

This preliminary work is aimed at investigating numerically the behaviour of unreinforced masonry walls strengthened through the use of metallic tie rods. In the first part, the improvement of strength is studied by evaluating the increase in shear resistance for low vertical action values, which is the most critical state for unreinforced masonry. Tie rods are placed along diagonals of the walls, as to maximize their effect on the overall strength and on recentering capabilities of piers. Subsequently, by using non-linear dynamic analyses carried out on a masonry wall, the importance of the axial forces acting on retrofitted piers during a seismic event is highlighted. It is shown that this becomes particularly important in the presence of a significant vertical component due to seismic actions. All the analyses are carried-out with non-linear material models, as to investigate the capacity in post-elastic field. Finally, the recentering capabilities and cyclic response of strengthened piers using tie rods are evaluated, on the basis of the residual transversal displacements measured at the end of numerical simulations. Results show improvements on the shear-displacements cyclic behaviour of reinforced piers, including better recentering capabilities, enhancing masonry performance under seismic conditions.

Though flexible diaphragms play a role in the seismic behaviour of unreinforced masonry buildings, the effect of the connections between floors and walls is rarely discussed or explicitly modelled when simulating the response of such buildings. These flexible diaphragms are most commonly timber floors made of planks and beams, which are supported on recesses in the masonry walls and can slide when the friction resistance is reached. Using equivalent frame models, we capture the effects of both the diaphragm stiffness and the finite strength of wall-to-diaphragm connections on the seismic behaviour of unreinforced masonry buildings. To do this, we use a newly developed macro-element able to simulate both in-plane and out-of-plane behaviour of the masonry walls and non-linear springs to simulate wall-to-wall and wall-to-diaphragm connections. As an unretrofitted case study, we model a building on a shake table, which developed large in-plane and out-of-plane displacements. We then simulate three retrofit interventions: Retrofitted diaphragms, connections, and diaphragms and connections. We show that strengthening the diaphragm alone is ineffective when the friction capacity of the wall-to-diaphragm connection is exceeded. This also means that modelling an unstrengthened wall-to-diaphragm connection as having infinite stiffness and strength leads to unrealistic box-type behaviour. This is particularly important if the equivalent frame model should capture both global in-plane and local out-of-plane failure modes.

Malawi is an earthquake-prone country that lies within the East African Rift. A large proportion of its population lives in non-engineered single-storey constructions made of clay bricks and low-strength mortar. Walls are typically single-skin and often lack adequate wall-to-wall connections, leaving them vulnerable to seismic actions. This work reports a comprehensive study on the seismic fragility of unreinforced masonry buildings of the Malawi housing stock. The probability of exceeding different levels of in-plane/out-of-plane damage is estimated by considering the aleatory and epistemic uncertainties of the problem. Inter-building and intra27 building variability are accounted for by adopting material test results and building survey data collected in Malawi. The in-plane capacity of building walls is calculated through a finite element model that considers the orthotropic properties of masonry. The out-of-plane capacity is computed using an analytical solution, developed for walls in one way bending. In addition, record-to-record variability is considered. The new country-specific fragility models result more conservative that global estimates, which reflects the high vulnerability of Malawian masonry buildings. These fragilities can be integrated into catastrophe modelling platforms for earthquake risk assessment in Malawi and in the wider East African region.

Performance-based design plays a significant role in the structural and earthquake engineering community to ensure both safety and economic feasibility. Its application to masonry building design/assessment is limited and requires straightforward rules considering the characteristics of masonry behavior. Nonlinear static procedures mainly cover regular frame system structures, and their application to both regular and irregular masonry buildings require further investigation. The present paper addresses two major issues: (i) the definition of irregularity in masonry buildings, and (ii) the applicability of classical nonlinear static procedures to irregular masonry buildings. It is observed that the irregularity definition is not comprehensive and has different descriptions among the seismic codes as well as among researchers, particularly in the case of masonry buildings. The lack of global language may result in the misuse of the procedures, while adjustments may be essential due to irregularity effects. Therefore, irregularity indices given by different codes and research studies are discussed. Furthermore, an overview of nonlinear static procedures implemented within the framework of the performance-based approach and improvements proposed for its application in masonry buildings is presented., This research was funded by the Portuguese Foundation for Science and Technology FCT, grant number SFRH/BD/143949/2019 and PTDC/ECI-EGC/29010/2017.

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 describes the derivation of fragility curves useful for the seismic risk analyses of existing unreinforced masonry buildings inserted in aggregate. The L-shaped examined aggregate consists of three adjacent structural units that may mutually interact during seismic events. The seismic assessment is focused on the corner unit. The effects of different connection types between the adjacent units on the structural response were investigated. The seismic vulnerability of the masonry aggregate was assessed through nonlinear dynamic analyses (NDA) performed according to the multi-stripes approach. Both the in-plane and out-of-plane mechanisms were analyzed. The in-plane response of the corner unit is assessed through a 3D equivalent frame model of the entire aggregate, while the evaluation of its out-of-plane response makes use of the rigid-block assumption. Although evaluated in a separate way, the NDAs performed on the latter are based on the time histories derived from the global 3D model. The results are then processed in order to derive fragility curves, firstly, of the single failure mechanisms and, then, of the overall combined behavior. To this aim, various performance conditions are examined. For the reference building, the damage limit state is mainly governed by the in-plane behavior, while the collapse limit state by out-of-plane mechanisms. Moreover, the higher the connection level between adjacent structural units, the higher the interaction between in-plane and out-of-plane mechanisms at the collapse limit state.

The seismic assessment of unreinforced masonry (URM) buildings with cavity walls is a relevant issue in many countries, such as in Central and Northern Europe, Australia, New Zealand, China and several other countries. A cavity wall consists of two separate parallel masonry walls (called leaves) connected by metal ties: an inner loadbearing wall and an outer veneer having mostly aesthetic and insulating functions. Cavity walls are particularly vulnerable structural elements. If the two leaves of the cavity wall are not properly connected, their out-of-plane strength may be significantly smaller than that of an equivalent solid wall with the same thickness. The research presented in this paper focuses on a mechanical model developed to predict the failure mode and the strength capacity of metal tie connections in masonry cavity walls. The model considers six possible failures, namely tie failure, cone break-out failure, pull-out failure, buckling failure, piercing failure and punching failure. Tie failure is a predictable quantity when the possible failure modes can be captured. The mechanical model for the ties has been validated against the outcomes of an experimental campaign conducted earlier by the authors. The mechanical model is able to capture the mean peak force and the failure mode obtained from the tests. The mechanical model can be easily adopted by practising engineers who aim to model the wall ties accurately in order to assess the strength and behaviour of the structures against earthquakes. Furthermore, the proposed mechanical model is used to extrapolate the experimental results to untested configurations, by performing parametric analyses on key parameters including a higher strength mortar of the calcium silicate brick masonry, a different cavity depth, a different tie embedment depth, and solid versus perforated clay bricks.

In recent years, the number of human-induced earthquakes in Groningen, a large gas field in the north of the Netherlands, has increased. The majority of the buildings are built by using unreinforced masonry (URM), most of which consists of cavity (i.e. two-leaf) walls, and were not designed to withstand earthquakes. Efforts to define, test and standardize the metal ties, which do play an important role, are valuable also from the wider construction industry point of view. The presented study exhibits findings on the behavior of the metal tie connections between the masonry leaves often used in Dutch construction practice, but also elsewhere around the world. An experimental campaign has been carried out at Delft University of Technology to provide a complete characterization of the axial behavior of traditional connections in cavity walls. A large number of variations was considered in this research: two embedment lengths, four pre-compression levels, two different tie geometries, and five different testing protocols, including monotonic and cyclic loading. The experimental results showed that the capacity of the connection was strongly influenced by the embedment length and the geometry of the tie, whereas the applied pre-compression and the loading rate did not have a significant influence.

The assessment of the seismic vulnerability of masonry buildings requires reliable and computationally efficient numerical models. Different modelling strategies can be adopted when studying the global response of these structures, such as Continuum Constitutive Laws Models (CCLM) belonging to Finite Element (FE) models, which may be very accurate but whose use in practice presents several issues (high computational burden, requirement of many input data), and Equivalent Frame (EF) Models, that, even if based on strong simplifications, are now widespread in engineering practice, thanks to their computational efficiency and the need of few mechanical parameters for the structural analysis. The paper discusses the consistent use of these modelling techniques for the seismic analysis of masonry structures . To this aim, a comparison of two approaches (CCL and EF models) is presented focusing at first the attention on the calibration of the constitutive laws through analyses on single panels and then moving to the validation of some simplified assumptions made in the EFM through the analysis of a 2D regular URM wall. For the aim of validation, the CCL model is considered as the reference solution making an accurate comparison with the EF model in terms of generalized forces, drift and damage occurred at element scale and of pushover curve at global scale.

Out-of-plane (OOP) failure of unreinforced masonry (URM) walls in two-way bending was widely observed after natural hazards such as earthquakes. Of various crucial factors influencing the force capacity of URM walls in OOP two-way bending (force capacity being defined as the wall peak force in terms of pressure), the pre-compression and aspect ratio (defined as the wall height to length with the height kept constant) have not been sufficiently studied. To better understand their influence, an extensive numerical study was conducted by employing a detailed 3D brick-to-brick modelling method. First, a set of monotonic quasi-static tests on full-scale walls was taken as references for calibration and validation. The numerical results matched well with the experimental results in terms of initial stiffness, force capacity and crack pattern. Afterwards, the validated model was adopted to carry out a parametric study. Results show that the force capacity of the URM walls in OOP two-way bending is exponentially related to the aspect ratio and linearly related to the pre-compression. Besides, the influence of the pre-compression and aspect ratio on the force capacity can be interdependent. Additionally, when the pre-compression is relatively low, a wall does not crack in a localized manner into several rigid plane plates at the force capacity. Instead, the deformed shape of the wall approximates a curved surface, indicating distributed rather than localized cracking at force capacity. Furthermore, the force capacity is much higher than the residual force when the rigid-plates crack pattern is formed in the post-peak stage. The parametric study also shows that torsional failure of bed joints is the predominant failure mechanism for URM walls in OOP two-way bending, and its contribution to the force capacity generally increases as the pre-compression or aspect ratio increases. Finally, the numerical results were compared with the predictions by three major analytical formulations, namely Eurocode 6, Australian Standard for Masonry Structures (AS 3700) and Willis et al. (2006). As a result, the relations between the force capacity and the aspect ratio or pre-compression derived from the numerical models could not be accurately predicted by the analytical formulations. Based on previous results, recommendations on improving the analytical formulations were proposed.

Nowadays, existing masonry buildings are frequently modified to satisfy living demands. These modifications may require the addition of new windows or doors in walls of structural functionality. In engineering practice, such modifications are generally designed and verified for vertical loads while, for seismic loads, the changes in the walls' structural behaviour are not yet fully understood. Consequently, current design may incorrectly estimate the in-plane response of the perforated walls. This paper presents an evaluation of the effects of the introduction of new openings in masonry walls under in-plane loads by a numerical and experimental approach. Two parameters are considered for the numerical studies: opening size and eccentricity. The results show that the loss in stiffness and strength due to new openings are proportional to the opening area and that the eccentricity might change the wall response going from rocking to shear dominant behaviour, depending on the load direction.

Constructions built with partially grouted reinforced masonry (PG-RM) shear walls are common in several countries, and consequently, different construction solutions can be expected. In this context, one of the main differences detected is the type of horizontal steel reinforcement used. The most traditional options consist of bed-joint reinforcement and bond-beam reinforcement. Despite the advances in this research area, there is little experimental evidence to determine which of these horizontal reinforcement schemes exhibits a superior performance under seismic loads. Thus, the research described in this paper focused on assessing and comparing the seismic performance of PG-RM shear walls with different horizontal reinforcement options. For this purpose, four concrete masonry walls with an aspect ratio of 0.86 were tested undergoing constant axial pre-compression and quasi-static cyclic incremental lateral displacements. The tested walls had the same horizontal reinforcement ratio but different layouts (only bed joint reinforcement, only bond beam reinforcement, and a combination of them). The other design characteristics remained constant. The obtained results were analyzed in terms of the force-displacement curves and seismic performance parameters such as the maximum resistance, stiffness decay, energy dissipation, and equivalent viscous damping ratio. In addition, a comparative analysis of damage progression of the tested walls was carried out using the digital image correlation (DIC) technique. The tested walls experienced progressive deterioration of the lateral stiffness in proportion to drift increments regardless of the reinforcement scheme. Once achieved the lateral resistance, the degradation of the behavior accelerated, turning into a rather unpredictable response. Employing different horizontal reinforcement layout showed no influence on the lateral capacity of the walls when the same horizontal reinforcement ratio and material qualities are used. It was also observed that the distributed bed-joint reinforcement was better than the bond-beam reinforcement layout in controlling crack widths. Additionally, a combination of bond-beams and bed-joint reinforcement seems to be the most suitable reinforcement strategy based on hysteretic behavior, energy dissipation capacity, and ductility. The presented experimental evidence is promising, although further studies are required in order to promote its use in design codes and construction projects.

Unreinforced masonry (URM) structures are vulnerable to earthquakes; thus, materials and techniques for their strengthening and restoration should be developed. However, the materials used in some of the existing retrofitting technologies for URM and the waste produced at its end-of-life are unsustainable. The production of ordinary Portland cement (OPC) worldwide has enormously contributed to the global carbon footprint, resulting in persistent environmental problems. Replacing OPC with geopolymers, which are more sustainable and environmentally friendly, presents a potential solution to these problems. Geopolymers can replace the OPC component in engineering cementitious composites (ECC), recommended to strengthen and restore URM structures. In the present paper, the state-of-the-art knowledge development on applying geopolymers in URM structures is discussed. The discussion is focused on geopolymers and their components, material characterization, geopolymers as a strengthening and restoration material, and fiber-reinforced geopolymers and their application to URM structures. Based on this review, it was found that the mechanical properties of geopolymers are on par with that of OPC; however, there are few studies on the mentioned applications of geopolymers. The characterization of geopolymers’ mechanical and physical properties as a restoration material for URM structures is still limited. Therefore, other properties such as chemical interaction with the substrate, workability, thixotropic behavior, and aesthetic features of geopolymers need to be investigated for its wide application. The application method of geopolymer-based ECC as a strengthening material for a URM structure is by grouting injection. It is also worth recommending that other application techniques such as deep repointing, jacketing, and cement-plastering be explored.

The authors developed two types of block systems consisting only of main block and key block without joint mortar to improve the seismic performances and to enhance the workability. Two types of block systems have different key block shapes: one is the peanut shape, and the other is the dumbbell shape. The proposed block systems have a half-height difference between the main block and the key block to significantly improve seismic performance compared to typical masonry walls with joint mortar. In this study, in order to evaluate the in-plane seismic performance of the proposed block systems, two types of block walls are experimentally investigated, including the typical block wall. In the tests, three full-scale, single-story specimens are tested under in-plane cyclic loading, and failure patterns and cracks are carefully observed. In this paper, the in-plane loading bearing capacity, energy dissipate capacity and reuse ratios of block walls are discussed in detail. As a result, the deformability, energy absorption capacity and reuse ratio of the proposed block systems were considerably higher than those of a typical block system.

This paper presents an overview of the experimental results obtained by combined in-plane/out-of-plane (IP/OOP) tests carried out on robust clay masonry infill walls. The combined tests were carried out on eight full-scale one-bay, one-story infilled reinforced concrete (RC) frames, plus one reference RC bare frame. In four cases, the masonry walls fully fill the RC frame: two walls are made of unreinforced masonry (URM), whereas the other two are made of reinforced masonry (RM), with both vertical and horizontal reinforcement. Each pair of specimens was tested up to different levels of IP drift before carrying out the OOP tests. Four other specimens, still made of URM and RM walls, are characterized by the presence of a central opening, and in one case, the effect of a lintel is analyzed. On the basis of the tests carried out, an analytical model was developed for the analysis of the OOP behavior. It was used to calibrate IP damage degradation models based on the experimental results to define limits for the applicability of well-known flexural and arching mechanism models for the evaluation of the OOP capacity of the infill walls and to evaluate the efficiency of vertical reinforcement. In this work, the experimental campaign is presented, and the results of both experimental tests and numerical analyses are discussed.

This data article provides experimental data obtained from the incremental dynamic shake-table testing of four single leaf unreinforced masonry (URM) walls constructed in Calcium Silicate (CS) bricks reported in “Two-way bending experimental response of URM walls subjected to combined horizontal and vertical seismic excitation” [1] . These walls were tested in the second phase of a larger experimental campaign addressing the out-of-plane (OOP) response of full-scale URM panels in two-way bending configurations at EUCENTRE, Pavia, Italy. Data corresponding to the first phase of testing for four single leaf and one cavity wall has already been made available through Tomassetti et al. [2] and the information necessary to interpret these results can be found in Graziotti et al. [3] . The walls of the tests reported in this data article were constructed in an intentionally weakened mortar but using the same Calcium Silicate (CS) bricks as Graziotti et al. [3] . The walls were also tested in boundary conditions that were not addressed in [3] and a specimen was also subjected to simultaneous horizontal OOP and vertical seismic excitation in one of the tests. Videos documenting the failure of specimens tested in both phases of the experimental campaign can be viewed online on YouTube [4] .

Equivalent frame models are an effective tool for the seismic assessment of existing masonry structures. Due to their simplicity, these models can be used to perform multiple nonlinear dynamic analyses, accounting explicitly for different sources of modeling and input uncertainty. In the past, equivalent frame models have been used to effectively estimate the global response of buildings whose behavior is dominated by in-plane failure modes of piers and spandrels. The recent development of a three-dimensional macroelement formulation for modeling both the in-plane and out-of-plane response extends the use of equivalent frame models to the additional study of local out-of-plane mechanisms of a building. This work applies the newly developed formulation, implemented in OpenSEES (McKenna et al., 2000), to the modeling of two shaking table tests on a stone masonry building and on a modern mixed concrete-unreinforced masonry structure. Since the approach explicitly accounts for the quality of connections in the building (i.e., wall-to-wall and floor-to-wall connections), specific elements and material models were developed for modeling these connections in an equivalent frame idealization of the three-dimensional structure. Through comparison with the experimental results, the performance of the modeling approach is discussed, and the sensitivity of the response to the major sources of modeling uncertainty (quality of connections, damping model) is assessed. The comparisons show that these new equivalent frame models can capture the onset of out-of-plane failure for historical structures with poor floor-to-wall connections and for modern URM buildings with stiff RC slabs, where the slab can uplift from the URM wall, which leads to changing static and kinematic boundary conditions of the out-of-plane loaded wall. The results further show that 1–2% of damping leads to good agreements with the experimental results if initial stiffness proportional Rayleigh damping is used.

The weakness of tensile strength and high weight in masonry structures under the dynamic loads of earthquakes have always led to structural damage, financial losses, injuries and deaths. In spite of the cheap and affordable masonry materials, it has been very limited their use in constructions over the past three decades. However, common masonry materials are still found in monumental and historical structures, deteriorated texture and rural buildings. Identifying the seismic behaviour and the probability of the structural damage is vital for pre-earthquake seismic risk reduction of urban areas and the rapid post-earthquake assessment. The earthquake event occurred in Ezgeleh on 2017 November 12th with Mw=7.3 triggered the greatest damage in the Sarpol-e-zahab city at a distance of about 37 kilometres from the epicentre. Post-earthquake reconnaissance, microtremor analysis and rapid visual inventory of structural damages in different zones were performed by the research teams. In the present study, the strong ground motion, the peak ground acceleration and its corresponding intensity distribution, which are based on the site response analysis in different parts of the city, are introduced. Afterward, damage probability matrices of different types of masonry buildings, namely unreinforced masonry and confined masonry buildings, are determined for both bins of peak ground accelerations and intensities. Finally, the fragility curves of two types of masonry structures are extracted based on RISK-UE level 1 (LM1) method by assuming beta distribution to estimate the probability distribution function of the damage. These curves are useful in assessing pre-earthquake possible damages in masonry structures with similar construction methods and similar materials to reduce seismic risks.

Traditional unreinforced masonry (URM) constructions still represent an important part of the school building stock in several low-income countries including Nepal. Unfortunately, their intrinsic vulnerability impacts negatively on the resilience of cities and local communities. Observations after major seismic events have shown that the predominant mode of failure is the out-of-plane (OOP) of the weak and loosely connected perimeter masonry walls which typically leads to partial or global collapse. Starting from this evidence, a closed-form analytical approach is presented aimed at deriving the OOP force-displacement response of URM walls for different boundary conditions and vertical loads. The novel analytical solution is successfully validated with the results of seventeen OOP experimental tests on URM walls available in the literature. Then, referring to a case-study Nepalese school building, capacity curves of the constituting walls are derived and adopted for the vulnerability assessment of the structure through the Capacity Spectrum Method (CSM) where equivalent hysteretic damping is calibrated with available OOP shaking table test results. Lastly, PGA capacities for different damage states are successfully compared with median values from observational fragility curves.

Reinforced masonry walls are commonly used as a primary lateral load resisting system in buildings in regions of moderate or high seismicity. Mortarless reinforced masonry (MLRM) walls are constructed using concrete masonry units placed without mortar and then interconnected by concrete grout. The absence of mortar can overcome several issues during the construction of conventional reinforced masonry walls. Previous research mainly focused on mortarless systems using three-dimensional interlocking blocks without vertical reinforcement. In this study, a total of six MLRM walls were constructed and tested under cyclic loadings to investigate their seismic behaviour. Experimental parameters included axial load ratio, shear span ratio, and vertical reinforcement ratio of the walls. Test results showed that the MLRM walls exhibited high stiffness, good deformation capacity, and reasonable energy dissipation capacity. The response of all six walls under cyclic loadings was controlled by 3–4 cracks formed at bed joints between the concrete masonry units, and their failure was dominated by flexure with the occurrence of slight shear sliding. The load-displacement envelope, strength, and energy dissipation of all tested MLRM walls are discussed.

In this paper, a novel numerical procedure is proposed for the force-displacement description of out-of-plane collapse in masonry structures. The numerical procedure herein proposed represents one first attempt to couple limit analysis-based solutions to displacement-based evolutive analysis strategies. Limit-analysis based solutions are considered trustworthy to investigate collapse mechanisms in masonry structures, even though they cannot be used in displacement-based seismic assessment procedures (e.g. pushover analysis), while displacement-based evolutive analysis strategies (e.g. block-based and anisotropic continuum approaches), which can undertake this last task, are typically computationally demanding and their mechanical characterization is often very challenging. In this research, a genetic algorithm NURBS-based adaptive homogenized upper bound limit analysis is firstly adopted to compute the collapse mechanism that the structure (of any geometrical complexity) experiences for a given loading condition. Then, the 3D geometry of the collapse mechanism is imported in incremental-iterative step-by-step evolutive analysis frameworks to perform pushover analysis. In particular, two numerical modelling approaches are conceived to this aim, both lumping all the mechanical nonlinearities into tight zones located in correspondence of the cracks defined in the collapse mechanism previously computed. The first one uses 3D plastic damaging strips governed by a standard nonlinear continuum constitutive law. The second approach adopts non-standard zero-thickness contact-based interfaces governed by a cohesive-frictional contact behaviour previously developed by the authors for the brick-to-brick mechanical interaction. A number of meaningful structural examples show the effectiveness of the numerical procedure proposed. Pushover curves obtained through different modelling strategies are also critically compared.

Equivalent frame method (EFM) is a viable modelling option for global seismic analysis of masonry buildings in comparison to more refined techniques, such as finite elements (FE), especially in professional practice [1, 2, 3]. EFM takes advantage of a building’s geometric regularity, both in plan and elevation, as well as of the good quality of masonry and floors stiffness, as required for the activation of box-like behaviour under seismic loads. However, typical vulnerabilities in existing unreinforced masonry (URM) buildings, e.g. highly flexible floors, openings too close one another, poor quality masonry, isolated pillars or non-vertically aligned walls, limit the effectiveness of EFM application. Recently, many studies have been devoted to expanding the possibilities of applying EFM to buildings which do not meet box-behaviour hypotheses [4, 5, 6].

In this study, a novel computational modeling strategy is proposed to estimate the lateral load capacity and behavior of unreinforced masonry (URM) structures. All commonly noted failure mechanisms are captured via the proposed modeling strategy using the discrete element method (DEM) in three-dimensions (3D). Masonry walls are represented as a system of elastic discrete blocks, where the nodal velocities are evaluated by integrating the equations of motion using the central difference method. Then, the mechanical interactions among adjacent blocks are examined utilizing the relative contact displacements and employed in the contact stress calculation. Through this research, a new stress-displacement contact constitutive model is considered and implemented in the commercial software 3DEC, which includes softening stress-displacement behavior for tension, shear, and compression along with the fracture energy concept. The results of the discontinuum models are validated on small- and large-scale experimental studies available in the literature with good agreement. Furthermore, important inferences are made regarding the effect of block size, the number of contact points, and contact stiffness values for robust and accurate simulations of masonry walls., (undefined)

Investigations of post-seismic events show that the collapse of walls in out-of-plane (OOP) two-way bending can be one of the most predominant failure mechanisms for unreinforced masonry (URM) structures. To assess the force capacity of URM walls in OOP two-way bending, various analytical formulations have been developed during past decades. However, the accuracy and the application range of these analytical formulations have been evaluated against only a limited number of experiments. For this purpose, a dataset of 46 testing specimens from 8 international testing campaigns was created and used to evaluate current analytical formulations, namely Eurocode 6 based on the yield line method, Australian Standard AS3700 based on the virtual work method, and two other virtual work formulations related to AS3700. A general comparison shows that within the listed dataset, AS3700 overall provides the most accurate predictions. More specifically, AS3700 is the most accurate assessing walls assumed to be partially clamped and walls with openings. Testing specimens were divided into groups to study the influence of crucial factors, such as material properties, boundary conditions, pre-compression, aspect ratio and openings. However, only in a few cases clear trends were identified from the testing data. Sensitivity studies were carried out to reveal how the analytical formulations assess the influence of the crucial factors on the force capacity of the walls. Results expose drawbacks and limitations of the considered analytical formulations. Eventually, potential directions for improving the accuracy and the application range of the analytical formulations are pointed out.

The shear properties of unreinforced masonry are key parameters used in order to understand the behaviour of these structures under horizontal actions. These characteristics are usually determined ...

A prolonged seismic sequence struck the regions of Central Italy between August 2016 and January 2017, causing several fatalities and widespread damage to the built environment. The main objective of this work was to study the structural and seismic behavior of "Pietro Capuzi" school, located in Visso, in the Marche region, which was severely damaged by the 2016-2017 Central Italy Earthquake. A 3D finite clement (FE) model of the entire school was prepared, adopting a macro-modeling approach to represent masonry materials. An eigenvalue analysis was initially performed in order to identify the dominant modes of vibration of the structure and to calibrate the numerical model according to the results of the dynamic identification tests. Afterwards, nonlinear static analyses were performed on the calibrated FE model to evaluate the seismic response of the structure. Finally, the numerical results obtained in terms of crack pattern and failure mechanisms were compared with the damage experienced by the building. The numerical model proved to accurately predict the seismic response exhibited by the structure during the past seismic events., The authors wish to express their gratitude to the Seismic Observatory of Structures, RELUIS and Ing. Serena Cattari of the University of Genova for the material provided for the development of the present work. The work was carried out thanks to the financial support of the European Commission within the framework of the SAHC master course. The authors are grateful to the SAHC Consortium and the University of Minho in Guimaraes (Portugal) for the support provided.

Tile vaults are unreinforced masonry structures made of thin bricks (tiles) and fast-setting mortar that can be constructed without the need of a formwork, except at the boundaries, making them inherently economic. Their slenderness and finishing make them also efficient and expressive. These qualities of tile vaulting can be enhanced by combining it with reinforced concrete creating a new composite system. The tile vault can be integrated in the final solution, as a permanent formwork, reducing construction costs and waste. A top layer of reinforced concrete rises up the strength of the composite system, whereas reinforcement reduces the thickness and opens the possibility to build structures with a formal language well beyond what is typically associated with masonry architecture. Therefore, several advantages make the system competitive compared to traditional reinforced concrete shells. This paper presents experimental research on the materials of this composite system and load tests on composite barrel vaults. The construction of full-scale prototypes has allowed a critical review of the construction process and has demonstrated the feasibility of the technique and its successful structural performance. Moreover, the analysis of these composite structures is carried out using Extended Limit Analysis of Reinforced Masonry (ELARM), provided that the reinforcement guarantees sufficient ductility. Furthermore, the data collected from the experimental research becomes a benchmark for the calibration of eventual further structural models. This work was supported by the Swiss National Science Foundation (SNSF, project number P2EZP2_181591). Second author is a Serra Húnter Fellow. This research was also sponsored by the construction company URCOTEX, from which Josep Brazo, Antonio Haro and Albert Martí are especially acknowledged. The construction of the prototypes was carried out together with Jordi Domènech, to whom the authors are very thankful as well. Christian Escrig and Luis Mercedes, from the UPC’s Laboratory for Technological Innovation in Structures and Materials (LITEM), are acknowledged too for their support during the load tests’ setup and during construction respectively. The authors are likewise thankful to Dr. Diego Aponte and Prof. Marilda Barra (UPC) for their help in the development of the concrete’s recipe and their valuable advice in this regard.

A non-linear discrete homogenized strategy is used to reproduce out-of-plane two-way bending shake table tests on full-scale unreinforced masonry walls. The numerical strategy represents unreinforced masonry walls as an assemblage of rigid quadrilateral plates connected through non-linear interfaces represented. The material response laws for these non-linear interfaces are derived from a homogenization procedure performed at the meso-scale by a finite-element plate model. This discrete model can simulate masonry orthotropy, full softening behaviour and failure. Bending and torsional deformation modes are represented. The performance of the numerical models in describing the response of the experimentally tested full-scale specimens is presented. The numerical strategy is then used to study the behaviour of unreinforced masonry walls in configurations hitherto untested. Such numerical results are then compared to state-of-the-art analytical approaches. Potential avenues of improvement for the implemented analytical methods are also highlighted.

In this paper, a two-step automated procedure based on adaptive limit and pushover analyses is developed for the seismic assessment of masonry structures. Inspired by an akin procedure previously developed by the authors for the out-of-plane behaviour, the procedure herein presented is extended to in-plane and combined in- and out-of-plane loading conditions, accounting also for the effect of masonry crushing failure. In the first step, an upper-bound adaptive limit analysis tool is used to predict the collapse mechanism (and the corresponding multiplier) of the structure given a certain loading condition. A novel ad-hoc routine is then developed and utilized for the automatic import of the collapse mechanism geometry of any complexity into a solid model ready to be used in a finite element framework. In the second step, cohesive-frictional contact-based interfaces are automatically inserted in the cracks of the collapse mechanism formerly obtained, and a pushover analysis is conducted to investigate the load–displacement response of the structure. A series of parametric analyses are conducted to highlight the effect of different mechanical assumptions. Finally, the effectiveness of the procedure proposed is shown on a full-scale masonry building case study.

In recent years, traditional masonry structures have been widely used in rural areas of China. However, they were found to have a poor seismic performance during earthquakes. In this study, a new prestressing technology was proposed and described in detail, and it was used in fully grouted concrete masonry wall systems to improve its seismic performance. The experimental work involved investigating the seismic response of four fully grouted reinforced concrete masonry wall systems, consisting of two symmetrically arranged reinforced block masonry walls, with different section types and prestressing technologies, when subjected to cyclic lateral force. Based on the test results, a flexure and ductile failure occurred in the specimens with a rectangular section, while a shear and brittle failure occurred in the specimens with a T-shape section. The prestressing technology had no significant effect on the failure state of the specimens, but it influenced the crack propagation, making cracks fine and densely covered. A symmetrical and obvious pinching effect was observed in the hysteretic response of all specimens. The average displacement ductility of the specimens varied within a range of values between 3.34 and 6.92, according to the section type of the specimens, and the prestressing technology improved the displacement ductility of the specimens. Moreover, the prestressing technology significantly improved the initial stiffness of the specimens, and the specimens with prestressing technology experienced a greater fall in the degradation of the normalized stiffness than the specimens without this technology throughout the loading process. In addition, the equivalent viscous damping of the specimens ranged between 8.2% and 10.8%, according to the section type. It could be concluded that the prestressing technology improved the energy dissipation of the specimens at the ascending stage, although it had no marked influence on the equivalent damping ratio of the specimens.

An experimental program on reinforced concrete masonry beams was conducted aiming to better understand the behavior of reinforced masonry beams. The beams were designed to fail in flexure, assessing cracking patterns, maximum displacement, ultimate bending moment, and maximum flexural and axial compression strain. The experimental program included 12 reinforced masonry beam tested under flexure and built with bond-beam and hollow concrete blocks. Also, two type of prism were built and tested; one type stacked into the block greater dimension allowing testing with compression in the same direction as in the beams; and the second type as standard grouted prisms. Results indicate an average masonry compression strength parallel to bed joint 25% lower than the masonry compression strength in the other direction (perpendicular to bed joints). There was a significant increase on the beam stiffness due to the construction of one more block course. The model used to calculate the ultimate bending moment led to values close to the experimental result (difference of about 15%). Finally, the ultimate average shortening strain of masonry at axial compression was 50% lower than at flexural compression. Resumo Com objetivo de contribuir com o melhor entendimento do comportamento de vigas de alvenaria estrutural armada, foi realizado o estudo experimental de vigas de alvenaria armada com blocos de concreto. Essas foram projetadas para ruptura à flexão, sendo analisando o modo de fissuração, a flecha, o momento fletor último, a deformação por encurtamento médio último da alvenaria na compressão simples e na flexão. Foi desenvolvido um programa experimental no qual foram ensaiadas, à flexão simples, 12 vigas de alvenaria estrutural armada confeccionadas com canaletas e blocos de concreto. Para comparação entre resistência à compressão da alvenaria paralela e perpendicular às juntas horizontais, foram confeccionados e ensaiados dois tipos de prismas; 4 prismas grauteados, confeccionados com a maior dimensão dos blocos na vertical, simulando a ocorrência das tensões de compressão nas vigas (paralelas às juntas horizontais), e 4 prismas convencionais grauteados. Resultados mostraram que, em média, a resistência à compressão da alvenaria paralela às juntas horizontais foi 25% menor comparada com a outra direção (perpendicular às juntas horizontais). Houve um aumento significativo da rigidez das vigas devido à inserção de mais uma fiada. O modelo utilizado para o cálculo do momento fletor último conduziu a valores próximos dos experimentais (diferença de aproximadamente 15%). E em média, o encurtamento último da alvenaria na compressão simples foi 50% menor do que na flexão.

International audience; We report on experimental and numerical investigations of textile reinforced mortar (TRM) strengthening systems, an innovative solution for reinforcing historical masonry structures. The experimental campaign presented in this paper is original and concerns two commercial TRM applications to single-leaf clay masonry panels. The proposed FE modelling is based on a multiscale approach with the possibility of simulating bed joints sliding and TRM-reinforcement debonding. This last phenomenon is frequently reported in the experimental literature and it has been observed also in our experimental tests. The numerical model is applied to study the behaviour of TRM reinforced masonry panels under diagonal compression tests.

An analytical rheological model capable of describing the loading speed dependent in-plane shear behaviour of a masonry multi-layer bed joint is presented in this paper. Such joints consist of a core soft layer protected by two thin extruded elastomer membranes, which in turn are placed in a bed mortar joint. The extruded elastomer membranes are employed to prevent and/or limit the deterioration of the core soft layer during the cyclic action observed in previous investigations. Joint behaviour is assumed to be linear elastic-perfectly viscoplastic and has been captured by a uniaxial model consisting of three elements: an elastic spring connected in series with the frictional slider and a dashpot (viscous damper). The rheological model is characterized by three material parameters that have been assessed from several series of monotonic and static-cyclic tests on small masonry specimens (triplets). In addition to these three parameters, the contraction of the thickness of multi-layer bed joint due to pre-compression has been considered too. Although model parameters are determined for the multi-layer bed joint with a rubber granulate core soft layer, the parameter space can be extended to the other types of core soft layer once the appropriate test data becomes available.

To assess the shear properties of masonry for existing buildings, the shove test method proposed by ASTM C1531 can be carried out, in which the load required to slide a single brick with respect to the surrounding masonry is measured. To control the vertical stress-state on the tested brick, two flat-jacks can be inserted in mortar bed joints in close proximity of it, thus prescribing a predefined level of compression. Although this test seems straightforward, uncertainties have not been resolved yet regarding the actual vertical compressive stress present on the tested brick and the effect of dilatancy. To gain a better insight into the shear-sliding behavior of masonry during the shove test, both experimental tests and numerical simulations were considered in the current research. To analyze these aspects and to precisely define a testing protocol, the experimental tests were performed in a controlled laboratory environment on a single wythe calcium silicate brick masonry wall. In parallel, numerical analyses were carried out using a simplified micro-modeling strategy, in which every brick was modelled, and the mortar joints were considered as zero-thickness interfaces. A composite interface model was used, including a tension cut-off, a Coulomb friction domain and a compressive cap. For the analyzed case study, the numerical results allowed to gain a better understanding of the aspects influencing the shear-sliding behavior of masonry during the shove test.

In this paper, a damaging block-based model is proposed for the numerical analysis of the cyclic behaviour of full-scale masonry structures. Solid 3D finite elements governed by a plastic-damage constitutive law in tension and compression are used to model the blocks, while a cohesive-frictional contact-based formulation is developed to simulate their cyclic interaction. The use of tests on small-scale specimens to calibrate the mechanical properties of the numerical model is presented and discussed. The tests belong to a comprehensive experimental campaign performed on calcium silicate brick masonry. The calibrated models are used to simulate in-plane and out-of-plane cyclic tests on masonry walls made of the same material, as well as a quasi-static cyclic pushover test on a full-scale terraced masonry house. The efficiency, the potentialities and the accuracy of the model here proposed are shown and discussed. The capability of explicitly representing structural details (e.g. running bonds) and any in-plane and through-thickness texture of masonry, which appears essential to study the response of masonry structures, is guaranteed by the block-based modelling approach. A good agreement between the numerical results and the experimental outcomes is observed. This allows to validate the model in the cyclic response as well as the strategy proposed for its mechanical characterization.

Through-the-thickness (TT) confinement of masonry and concrete panels by composite or steel reinforcements, aiming at seismic retrofit of existing structures, has recently growth in popularity. However, structural design of transversal reinforcements, modelled as an homogeneized material, is often performed by neglecting the cyclic nature of seismic actions and by using static approaches. For this reason, a proper strength hierarchy between the confined core material and the confining devices should be accounted for in order to ensure that the retrofit system remains effective until the crisis of the core material is attained. This research introduces strength hierarchy conditions for TT-confinement systems, made of materials exhibiting a nonlinear behavior, aiming at determining the minimum strength required for uniaxial confining devices. The relevant relationships, theoretically derived by assuming a Drucker Prager constitutive model for the confined material and by enforcing equilibrium and compatibility conditions between the core and the confining devices, are characterized by simple mechanical parameters, usually available in common practice applications, familiar to most of the designers. Numerical examples confirm the effectiveness of the proposed provisions.

The seismic behaviour of masonry structures is, as well-known, strongly influenced by axial stresses. During a seismic event, variations in axial loading cause in fact a change, that can be substantial, in the response in the lateral resistance capacity of masonry panels. Moreover, the axial stress can be modified by the vertical component of the seismic input during an event, which can amplify the strength variations, in particular if there is a near-fault excitation. In general, such vertical component is neglected in a traditional design. In this work, the influence of the vertical component of a seismic event is evaluated by measuring the lateral resistance of masonry piers. Such influence is estimated through a cyclic phenomenological model which calculates in an analytical way the lateral strength of a masonry panel on the base of the actual axial loading, reached step-by-step during a non-linear analysis. This model is used to simulate the cyclic behaviour of an unreinforced masonry facade made of 3 piers, having the same section for 2 floors and connected by rigid spandrels. The wall, representative of a typical masonry facade, is subjected to a series of earthquake records, with and without the vertical component of the seismic input. The differences in the responses are quantified through the use of seismic reduction factors, in such a way to satisfy the checking of the piers adopting the current design codes.