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.     

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.     

Modelling the out‐of‐plane seismic behaviour of masonry walls by rigid elements

A computational model for evaluating the dynamical response and the damage of large masonry walls subjected to out‐of‐plane seismic actions is presented. During earthquakes, these actions are often the main cause of damage for the front wall and lateral walls of old masonry‐built churches and monuments. Since the crack patterns often tend to subdivide the plane walls into a number of blocks, the model assumes such walls as a series of quadrilateral plane rigid elements connected to each other in the middle of their adjoining sides. Only the out‐of‐plane displacements are considered, and the connections are regarded as spherical elasto‐plastic joints which allow rotations whose axis is in the plane of the undeformed wall. The hysteretic characteristics of these joints are defined so as to approximate the brittle behaviour of masonry material and the degradation due to cyclic loadings. The numerical results obtained using a limited number of elements show that the global out‐of‐plane response of the masonry walls and the mechanical degradation at each connection are in accord with the observed behaviour of real churches hit by strong earthquakes. Copyright © 2000 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 situ cyclic tests on existing stone masonry walls and strengthening solutions

The present work reports on an in situ experimental test campaign carried out on abandoned traditional masonry houses after the 9th July 1998 earthquake that seriously hit the Faial island of Azores. For the testing purposes, an experimental test setup was developed based on a self‐equilibrated scheme, which is herein described reporting on the advantages and drawbacks of this in situ test setup. Five specimens were tested aiming at characterizing the out‐of‐plane behavior of stone masonry walls and strengthening solutions recommended for post‐earthquake interventions. A detailed comparison between solutions' efficiency is presented including a cost vs benefit analysis. In order to assess the efficiency of the developed test setup for other applications on stone masonry walls, an in‐plane test on an existing URM panel is also presented. Several related issues are discussed, namely the advantages of dealing with the real boundary conditions and the capacity of providing valuable information of the response, as well as a detailed analysis of the obtained results. The authors believe that this work provides an increase in knowledge on the seismic behavior of the existing masonry constructions, resulting from the development of an in situ test setup and the efficiency quantification of strengthening solutions. Therefore, the work is thought to positively contribute for the preservation of architectural heritage and for its seismic vulnerability reduction. Copyright © 2010 John Wiley & Sons, Ltd.     

Empirical‐based out‐of‐plane URM infill wall model accounting for the interaction with in‐plane demand

The role of masonry infills in the seismic behavior of reinforced concrete buildings has been widely studied in terms of their strength and stiffness contribution in the in‐plane (IP) direction, while fewer studies have been carried out on their response and modeling in the out‐of‐plane (OOP) direction. In this paper, the state of the art in code and literature provisions regarding infills' OOP capacity and seismic demand is presented, together with a review of the experimental tests that have been carried out to investigate infills' OOP behavior and the effects of IP‐OOP interaction. This review aims to collect an experimental database that is used to evaluate the effectiveness of literature and code provisions and to propose a semiempirical approach both for predicting infills' OOP strength, stiffness, and displacement capacity and for modeling the effects of IP displacement demand on OOP behavior and vice versa. Then, the state of the art on modeling of infills' OOP behavior and IP‐OOP interaction is presented together with a new macro model based on the proposed formulations and conceived to represent the IP and OOP behavior by taking into account the mutual interaction effects. Finally, the proposed model is used for an example application on two case‐study buildings, showing the effects of taking into account or neglecting the IP‐OOP interaction phenomena.     

Simulation of masonry out‐of‐plane failure modes by multi‐body dynamics

The seismic assessment of the local failure modes in existing masonry buildings is currently based on the identification of the so‐called local mechanisms, often associated with the out‐of‐plane wall behavior, whose stability is evaluated by static force‐based approaches and, more recently, by some displacement‐based proposals. Local mechanisms consist of kinematic chains of masonry portions, often regarded as rigid bodies, with geometric nonlinearity and concentrated nonlinearity in predefined contact regions (unilateral no‐tension behavior, possible sliding with friction). In this work, the dynamic behavior of local mechanisms is simulated through multi‐body dynamics, to obtain the nonlinear response with efficient time history analyses that directly take into account the characteristics of the ground motion. The amplification/filtering effects of the structure are considered within the input motion. The proposed approach is validated with experimental results of two full‐scale shaking‐table tests on stone masonry buildings: a sacco‐stone masonry façade tested at Laboratório Nacional de Engenharia Civil and a two‐storey double‐leaf masonry building tested at European Centre for Training and Research in Earthquake Engineering (EUCENTRE). 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.     

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.     

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.     

Displacement‐based seismic analysis for out‐of‐plane bending of unreinforced masonry walls

This paper addresses the problem of assessing the seismic resistance of brick masonry walls subject to out‐of‐plane bending. A simplified linearized displacement‐based procedure is presented along with recommendations for the selection of an appropriate substitute structure in order to provide the most representative analytical results. A trilinear relationship is used to characterize the real nonlinear force–displacement relationship for unreinforced brick masonry walls. Predictions of the magnitude of support motion required to cause flexural failure of masonry walls using the linearized displacement‐based procedure and quasi‐static analysis procedures are compared with the results of experiments and non‐linear time‐history analyses. The displacement‐based procedure is shown to give significantly better predictions than the force‐based method. Copyright © 2002 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.     

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.     

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.     

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.     

In‐plane strength of unreinforced masonry piers

The definition of adequate simplified models to assess the in‐plane load‐bearing capacity of masonry piers, in terms of both strength and displacement, plays a fundamental role in the seismic verification of masonry buildings. In this paper, a critical review of the most widespread strength criteria present in the literature and codes to interpret the failure modes of piers (rocking, crushing, bed joint sliding or diagonal cracking) are proposed. Models are usually based on an approximate evaluation of the stress state produced by the external forces in a few points/sections and on its assessment with reference to a limit strength domain. The aim of the review is to assess their reliability by discussing the hypotheses, which they are based on (assumed stress states; choice of reference points/sections on which to assess the pier strength; characteristics of the limit strength domain) and to verify the conditions for their proper use in practice, in terms of both stress fields (depending on the geometry of the pier, boundary conditions and applied loads) and types of masonry (i.e. regular brick masonry vs rubble stone masonry). In order to achieve these objectives, parametric nonlinear finite element analyses are performed and different experimental data available in the literature are analysed and compared. Copyright © 2008 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.     

Cyclic testing of unreinforced masonry walls in two‐way bending

An experimental programme was conducted in which eight full‐scale unreinforced masonry walls were subjected to cyclic face loading using a system of airbags. Of the eight walls, six contained a window opening and four were subjected to vertical pre‐compression. Combined supports at the vertical and horizontal edges ensured that under face loading the walls underwent two‐way bending. The test walls were found to possess good post‐peak strength and displacement capacity as well as reasonable energy dissipation characteristics. Significant strength and stiffness degradation and non‐symmetry of strength in the positive and negative displacement directions were also evident. Discussion of the causes of the aforementioned trends and their implications towards the seismic response of masonry walls is provided. Copyright © 2006 John Wiley & Sons, Ltd.