Influence of boundary conditions on the out‐of‐plane response of brick masonry walls in buildings with RC slabs

In modern unreinforced masonry buildings with stiff RC slabs, walls of the top floor are most susceptible to out‐of‐plane failure. The out‐of‐plane response depends not only on the acceleration demand and wall geometry but also on the static and kinematic boundary conditions of the walls. This paper discusses the influence of these boundary conditions on the out‐of‐plane response through evaluation of shake table test results and numerical modelling. As a novum, it shows that the in‐plane response of flanking elements, which are orthogonal to the wall whose out‐of‐plane response is studied, has a significant influence on the vertical restraint at the top of the walls. The most critical configuration exists if the flanking elements are unreinforced masonry walls that rock. In this case, the floor slabs can uplift, and the out‐of‐plane load‐bearing walls loose the vertical restraint at the top. Numerical modelling confirms this experimentally observed behaviour and shows that slab uplift and the difference in base and top excitation have a strong influence on the out‐of‐plane response of the walls analysed. Copyright © 2016 John Wiley & Sons, Ltd.     

Nonlinear analysis of out‐of‐plane masonry façades: full dynamic versus pushover methods by rigid body and spring model

The paper proposes a systematic comparison between two methods of analysis that are well established in the field of earthquake engineering: nonlinear dynamic analysis and nonlinear static procedure (NSP), applied to the out‐of‐plane seismic response of two masonry façades representative of many ancient Italian churches. The comparison is based on extensive numerical analyses, which focus on the flexural and torsional mechanisms, while the in‐plane damage mechanisms and the possible detachment between the façade and the lateral walls because of a poor connection have been presently disregarded. The computations, both in the static and in the dynamic field, are based on a rigid body and spring model specifically implemented for this issue, computationally efficient and equipped with a realistic model of damage and hysteresis at the mesoscale. An innovative aspect of this study is the heuristic modelling of three‐wythe masonry, to include some typical texture effects on the macroscale nonlinear response. For each façade, two different masonry textures were considered, performing extensive dynamic analyses that offered a detailed overview about the performance under earthquakes of different intensities. In parallel, NSP and the classical N2‐based seismic assessment were applied. A critical discussion and comparison of the results of the two methods is presented to rationally appraise limits and opportunities. In particular, flexural and twisting out‐of‐plane mechanisms were clearly appraised in the dynamic field, whereas NSPs were not always able to describe the collapse, because they missed the partial failures determined by higher vibration modes, as could be expected. Copyright © 2012 John Wiley & Sons, Ltd.     

Generation of fragility curves for Turkish masonry buildings considering in‐plane failure modes

This study focuses on the seismic safety evaluation of masonry buildings in Turkey for in‐plane failure modes using fragility curves. Masonry buildings are classified and a set of fragility curves are generated for each class. The major structural parameters in the classification of masonry buildings are considered as the number of stories, load‐bearing wall material, regularity in plan and the arrangement of walls (required length, openings in walls, etc.), in accordance with the observations from previous earthquakes and field databases. The fragility curves are generated by using time history (for demand) and pushover (for capacity) analyses. From the generated sets of fragility curves, it is observed that the damage state probabilities are significantly influenced from the number of stories and wall material strength. In the second stage of the study, the generated fragility curves are employed to estimate the damage of masonry buildings in Dinar after the 1995 earthquake. The estimated damage by fragility information is compared with the inspected visual damage as assessed from the Damage Evaluation Form. For the quantification of fragility‐based damage, a single‐valued index, named as ‘vulnerability score’ (VS), is proposed. There seems to be a fair agreement between the two damage measures. In addition to this, decisions regarding the repair or demolition of masonry buildings in Dinar due to visual damage inspection are on comparable grounds with the relative measure obtained from VS of the same buildings. Hence, the fragility‐based procedure can provide an alternative for the seismic safety evaluation of masonry buildings in Turkey. Copyright © 2007 John Wiley & Sons, Ltd.     

Out‐of‐plane seismic behaviour of rocking masonry walls

The evaluation of the out‐of‐plane behaviour of unreinforced walls is one of the most debated topics in the seismic assessment of existing masonry buildings. The discontinuous nature of masonry and its interaction with the remainder of the building make the dynamic modelling of out‐of‐plane response troublesome. In this paper, the results of a shaking table laboratory campaign on a tuff masonry, natural scale, U‐shaped assemblage (façade adjacent to transverse walls) are presented. The tests, excited by scaled natural accelerograms, replicate the behaviour of external walls in existing masonry buildings, from the beginning of rocking motion to overturning. Two approaches have been developed for modelling the out‐of‐plane seismic behaviour: the discrete element method and an SDOF analytic model. Both approaches are shown to be capable of reproducing the experimental behaviour in terms of maximum rotation and time history dynamic response. Finally, test results and numerical time history simulations have been compared with the Italian seismic code assessment procedures. Copyright © 2011 John Wiley & Sons, Ltd.     

In‐plane and out‐of‐plane behavior of confined masonry walls for various toothing and openings details and prediction of their strength and stiffness

Eight half‐scale brick masonry walls were tested to study two important aspects of confined masonry (CM) walls related to its seismic behavior under in‐plane and out‐of‐plane loads. Four solid wall specimens tested to investigate the role of type of interface between the masonry and tie‐columns, such as toothing varying from none to every course. The other four specimens with openings were tested to study the effectiveness of various strengthening options around opening to mitigate their negative influence. In the set of four walls, one wall was infilled frame while the other three were CM walls of different configurations. The experimental results were further used to determine the accuracy of various existing models in predicting the in‐plane response quantities of CM walls. Confined masonry walls maintained structural integrity even when severely damaged and performed much better than infill frames. No significant effect of toothing details was noticed although toothing at every brick course was preferred for better post‐peak response. For perforated walls, provision of vertical elements along with continuous horizontal bands around openings was more effective in improving the overall response. Several empirical and semi‐empirical equations are available to estimate the lateral strength and stiffness of CM walls, but those including the contribution of longitudinal reinforcement in tie‐columns provided better predictions. The available equations along with reduction factors proposed for infills could not provide good estimates of strength and stiffness for perforated CM walls. However, recently proposed relations correlating strength/stiffness with the degree of confinement provided reasonable predictions for all wall specimens. Copyright © 2016 John Wiley & Sons, Ltd.     

Using the applied element method for modelling calcium silicate brick masonry subjected to in‐plane cyclic loading

The response of calcium silicate unreinforced masonry construction to horizontal cyclic loading has recently become the focus of experimental and numerical research, given its extensive use in some areas of the world that are now exposed to induced earthquakes (eg, north of the Netherlands). To assess the seismic behaviour of such construction, a relatively wide range of modelling methodologies are available, amongst which the discrete elements approach, which takes into account the intrinsic heterogeneity of a brick‐mortar assembly, can probably be deemed as the most appropriate computational procedure. On the other hand, however, since discrete elements numerical methods are based on a discontinuum domain, often they are not able to model every stage of the structural response adequately, and because of the high computational burden required, the analysis scale should be chosen carefully. The applied element method is a relatively recent addition to the discrete elements family, with a high potential for overcoming the aforementioned limitations or difficulties. Initially conceived to model blast events and concrete structures, its use in the earthquake engineering field is, of late, increasing noticeably. In this paper, the use of the applied element method to model the in‐plane cyclic response of calcium silicate masonry walls is discussed and scrutinised, also through the comparison with experimental results of in‐plane cyclic shear‐compression tests on unreinforced masonry walls.     

A macro‐model with nonlinear springs for seismic analysis of URM buildings

Seismic assessment of existing unreinforced masonry buildings represents a current challenge in structural engineering. Many historical masonry buildings in earthquake regions were not designed to withstand seismic loading; thus, these structures often do not meet the basic safety requirements recommended by current seismic codes and need to be strengthened considering the results from realistic structural analysis. This paper presents an efficient modelling strategy for representing the nonlinear response of unreinforced masonry components under in‐plane cyclic loading, which can be used for practical and accurate seismic assessment of masonry buildings. According to the proposed strategy, generic masonry perforated walls are modelled using an equivalent frame approach, where each masonry component is described utilising multi‐spring nonlinear elements connected by rigid links. When modelling piers and spandrels, nonlinear springs are placed at the two ends of the masonry element for describing the flexural behaviour and in the middle for representing the response in shear. Specific hysteretic rules allowing for degradation of stiffness and strength are then used for modelling the member response under cyclic loading. The accuracy and the significant potential of the proposed modelling approach are shown in several numerical examples, including comparisons against experimental results and the nonlinear dynamic analysis of a building structure. Copyright © 2016 John Wiley & Sons, Ltd.     

Simplified macro‐model for infill masonry walls considering the out‐of‐plane behaviour

One of the main challenges in earthquake risk mitigation is the assessment of existing buildings not designed according to modern codes and the development of effective techniques to strengthen these structures. Particular attention should be given to RC frame structures with masonry infill panels, as demonstrated by their poor performance in recent earthquakes in Europe. Understanding the seismic behaviour of masonry‐infilled RC frames presents one of the most difficult problems in structural engineering. Analytical tools to evaluate infill–frame interaction and the failure mechanisms need to be further studied. This research intends to develop a simplified macro‐model that takes into account the out‐of‐plane behaviour of the infill panels and the corresponding in‐plane and out‐of‐plane interaction when subjected to seismic loadings. Finally, a vulnerability assessment of an RC building will be performed in order to evaluate the influence of the out‐of‐plane consideration in the building response. Copyright © 2015 John Wiley & Sons, Ltd.     

Out‐of‐plane behaviour of a full scale stone masonry façade. Part 1: specimen and ground motion selection

The out‐of‐plane response of walls in existing stone masonry buildings is one of the major causes of vulnerability commonly observed in post‐earthquake damage surveys. In this context, a shaking table (ST) test campaign was carried out on a full‐scale masonry façade mainly focusing on the characterization of its out‐of‐plane overturning behaviour. The structure tested on the ST is a partial reproduction of an existing building from Azores, damaged during the 9 July 1998 Faial earthquake. The definition of the tested specimen as well as the selection of the input ground motion is reported in this paper. A specific emphasis is given to the definition of the time‐history to be applied during the tests because it was felt as an essential and crucial part of the work to obtain the desired overturning behaviour. The accelerogram to be imposed was selected from a large set of accelerograms (74) by means of a step‐by‐step procedure on the basis of several numerical analyses resorting to the rocking response of rigid blocks. A companion paper (Part 2) focuses on the ST test results and detailed data interpretation. Copyright © 2013 John Wiley & Sons, Ltd.     

Out‐of‐plane seismic response of vertically spanning URM walls connected to flexible diaphragms

A simplified numerical model was used to investigate the out‐of‐plane seismic response of vertically spanning unreinforced masonry (URM) wall strips. The URM wall strips were assumed to span between two flexible diaphragms and to develop a horizontal crack above the wall mid‐height. Three degrees of freedom were used to accommodate the wall displacement at the crack height and at the diaphragm connections, and the wall dynamic stability was studied. The equations of dynamic motion were obtained using principles of rocking mechanics of rigid bodies, and the formulae were modified to include semi‐rigid wall behaviour. Parametric studies were conducted that included calculation of the wall response for different values of diaphragm stiffness, wall properties, applied overburden, wall geometry and earthquake ground motions. The results of the study suggest that stiffening the horizontal diaphragms of typical low‐rise URM buildings will amplify the out‐of‐plane acceleration demand imposed on the wall and especially on the wall–diaphragm connections. It was found that upper‐storey walls connected to two flexible diaphragms had reduced stability for applied earthquake accelerograms having dominant frequency content that was comparable with the frequency of the diaphragms. It was also found that the applied overburden reduced wall stability by reducing the allowable wall rotations. The results of this study suggest that the existing American Society of Civil Engineers recommendations for assessment of vertically spanning walls overestimate the stability of top‐storey walls in multi‐storey buildings in high‐seismic regions or for walls connected to larger period (less stiff) diaphragms. Copyright © 2015 John Wiley & Sons, Ltd.     

Force–displacement response of in‐plane‐loaded URM walls with a dominating flexural mode

This article presents a new mechanical model for the non‐linear force–displacement response of unreinforced masonry (URM) walls developing a flexural rocking mode including their displacement capacity. The model is based on the plane‐section hypothesis and a constitutive law for the masonry with zero tensile strength and linear elastic behaviour in compression. It is assumed that only the compressed part of the wall contributes to the stiffness of the wall and therefore the model accounts for a softening of the response due the reduction of the effective area. Stress conditions for limit states are proposed that characterise the flexural failure. The new model allows therefore linking local performance levels to global displacement capacities. The limit states criteria describe the behaviour of modern URM walls with cement mortar of normal thickness and clay bricks. The model is validated through comparison of local and global engineering demand parameters with experimental results. It provides good prediction of the effective stiffness, the force capacity and the displacement capacity of URM walls at different limit states. Copyright © 2015 John Wiley & Sons, Ltd.     

Low‐seismic damage strategies for infilled RC frames: shake‐table tests

Unreinforced masonry (URM) infill panels are widely used as partitions in RC frames and typically considered as non‐structural elements in the design process. However, observations from recent major earthquakes have shown that under seismic excitation, the structural interaction between columns and infill walls can significantly alter the structural behaviour, thus causing catastrophic consequences. The purpose of this research was to propose and test an innovative low seismic damage detailing method, which isolates the infill panel from bounding columns with finite width vertical gaps during the infill panel construction phase and deploys steel wire connections in mortar layers anchored to columns. Taking into account the similitude requirements, a total of six one‐third scale, single‐storey single‐bay RC frames with different infill configurations and flexible connection details were carefully designed and tested on a shake‐table. Three real earthquake records were selected and scaled to ascending intensity levels and used as input signals. A series of thorough investigations including dynamic characteristics, hysteretic behaviour, failure mechanisms, out‐of‐plane vulnerabilities and the effect of different gap filling materials and load transfer mechanisms were rigorously studied. The experimental results indicate that the undesirable interaction between infill panels and bounding frame is significantly reduced using the proposed low seismic damage detailing concept. Direct shear failure of columns at an early stage is prevented, and structural redundancy at high levels of excitation can be provided. In general, the structural stability and integrity, and displacement ductility of infilled RC frames can remarkably be improved. Copyright © 2017 John Wiley & Sons, Ltd.     

Analytical model for the out‐of‐plane response of vertically spanning unreinforced masonry walls

An analytical model describing the flexural response of vertically spanning out‐of‐plane loaded unreinforced masonry walls is presented in this paper. The model is based on the second‐order Euler‐Bernoulli beam theory and captures important characteristics of the out‐of‐plane response of masonry walls that have been observed in experimental tests and from numerical studies but for which an analytical solution was still lacking: the onset and the evolution of cracking, the peak strength of the out‐of‐plane loaded walls, and the softening of the response due to P ?Δ effects. The model is validated against experimental results, and the comparison shows that the model captures both the prepeak and postpeak response of the walls. From the analytical model of the force‐displacement curve, a formula for the maximum out‐of‐plane strength of the walls is derived, which can be directly applied in engineering practice.     

Analysis of the in‐plane response of earthen masonry infill panels partitioned by sliding joints

The vulnerability of infilled frames represents a critical issue in many regions with high seismicity around the world where infills are typically made of heavy masonry as they are used for thermal control of the buildings because of their thermal inertia. In this context, the use of earthen masonry infills can give a superior performance because of their ability to regulate thermal‐hygrometric performance of the building and sustainability of its life‐cycle. This paper presents a numerical study on the seismic behaviour of infill walls made of earthen masonry and partitioned with horizontal wooden planks that allow the relative sliding of the partitions. The combination of the deformability of earthen masonry and the sliding mechanism occurring along the wooden planks gives a high ductility capacity to the in‐plane response of the infill and, at the same time, significantly reduces its stiffness and strength, as compared with traditional solid infills made of fired clay units. As a result, the detrimental interaction with the frame and the damage in the infill when subjected to in‐plane loading can be minimized. The numerical model is validated with results from an experimental study and is used to perform a parametric analysis to examine the influence of variations in the geometry and mechanical properties of the infill walls, as well as the configuration of the sliding joints. Based on the findings of this study, design guidelines for practical applications are provided, together with simple formulation for evaluating their performance. Copyright © 2016 John Wiley & Sons, Ltd.     

Free rocking response of a regular stone masonry wall with equivalent block approach: experimental and analytical evaluation

The evaluation of the dynamic behaviour of rocking elements is directly correlated to the energy dissipated because of the impacts at the base interface, which can be represented by means of a coefficient of restitution. This schematization is commonly accepted as representative of the out‐of‐plane response of stone masonry walls. An experimental campaign (in a lab environment) aiming at assessing the value of this coefficient for a sacco granite masonry wall is presented in this work. The rocking motion at a predefined bed joint level was induced in the tested specimens in order to validate a novel test setup designed to assess the coefficient of restitution value by means of a realistic reproduction of the rocking behaviour of a single element, under the hypothesis of an infinitely stiff system above the bed joint level. As the main objective of the work was to assess the rocking behaviour of a masonry wall that looses energy at the impacts at a certain joint level, the flexural behaviour was not desirable and had to be avoided. For this purpose, a test setup based on the equivalent block approach was developed. In the final section of this work, comparisons between experimental and numerical results are presented together with some preliminary conclusions on the appropriate modelling strategy and the values of the coefficient of restitution to be used for the seismic assessment of the out‐of‐plane rocking behaviour of this type of sacco stone masonry walls. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimation of load reduction factors for clay masonry walls

The in‐plane cyclic behaviour of three types of unreinforced clay masonry was characterized by means of laboratory tests on full‐scale specimens. The masonry walls were assembled with various bonding arrangements (head joints made with mortar pockets, dry head joints with mechanical interlocking, thin‐layer mortar bed joints), which are not yet inserted in seismic codes. Experimental behaviour was modelled with an analytical hysteretic model able to predict lateral load–displacement curves in case of shear failure of the unreinforced walls. According to the experimental results and those of the selected analytical model, parametric study to evaluate the reduction in lateral strength demand produced by non‐linear behaviour in masonry walls, i.e. the load reduction factor was carried out by non‐linear dynamic analyses. The calculated values of the load reduction factor were modest. The differences in values found for the three masonry types, although consistent with them, were not great. This may indicate that, in the ultimate limit state, the type of masonry cannot significantly affect the behaviour of an entire building. Copyright © 2009 John Wiley & Sons, Ltd.     

Performance of clay masonry veneer in wood‐stud walls subjected to out‐of‐plane seismic loads

This paper presents the findings of shaking‐table experiments conducted to examine the out‐of‐plane seismic performance of masonry veneer walls. Seven wall assemblies were tested, each consisting of a clay masonry veneer anchored to a wood‐stud backing. Design variables include the type of veneer ties, tie spacing, and presence or absence of mortar joint reinforcement and window opening. The walls were designed and constructed in accordance with current US code provisions. Results of the experiments show that failure of the corrugated ties is governed by pullout of the nails from the wood studs, while failure of the rigid ties is governed by detachment from the mortar joints or pull‐through of the screw heads through fastener holes. Both types of ties show satisfactory performance under ground motions corresponding to Design Basis and Maximum Considered Earthquakes representative of Seismic Design Category E. Although the rigid ties were stronger than the corrugated ties, they had wider vertical spacing and failed at a slightly higher seismic load. Observed extraction capacities of the nails show high variability, which merits attention. Joint reinforcement did not show any noticeable effect on the out‐of‐plane behavior of the veneer. Results of an analytical study have shown that the detachment of a veneer from the backing system is preceded by veneer cracking, which influences the distribution of tie forces, and that the vertical tie spacing influences the cracking load for the veneer. Copyright © 2010 John Wiley & Sons, Ltd.     

Explicit finite‐element analysis for the in‐plane cyclic behavior of unreinforced masonry structures

A simple constitutive model is proposed for an in‐plane numerical analysis of unreinforced masonry structures, which are subject to cyclic loading, by using explicit dynamic procedures. The proposed model is implemented by using two‐dimensional plane‐stress finite elements. Three different constitutive relations that are based on the total strain in the global material system are used. Cracking and crushing are controlled through normal strains, whereas shear is controlled through shear strain. Separate hysteretic rules are adopted for each mode of damage. A numerical analysis of masonry walls that are subject to cyclic loading has demonstrated that the use of explicit procedures in conjunction with the proposed model results in an acceptable accuracy when compared with the experimental results. Copyright © 2010 John Wiley & Sons, Ltd.