Bidirectional behavior of unreinforced masonry walls

Most of the studies related to the modeling of masonry structures have by far investigated either the in‐plane (IP) or the out‐of‐plane (OP) behavior of walls. However, seismic loads mostly impose simultaneous IP and OP demands on load‐bearing or shear masonry walls. Thus, there is a need to reconsider design equations of unreinforced masonry walls by taking into account bidirectional effects. The intent of this study is to investigate the bidirectional behavior of an unreinforced masonry wall with a typical aspect ratio under different displacement‐controlled loading directions making use of finite element analysis. For this purpose, the numerical procedure is first validated against the results of the tests on walls with different failure modes conducted by the authors. Afterward, the response of the wall systems is evaluated with increasing top displacement having different orientations. A set of 19 monotonic and three cyclic loading analyses are performed, and the results are discussed in terms of the variation of failure modes and load–displacement diagrams. Moreover, the results of wall capacity in each loading condition are compared with those of the ASCE41‐06 formulations. The results indicate that the direction of the resultant force, vectorial summation of IP and OP forces, of the wall is initially proportional to the ratio of stiffness in the IP and the OP directions. However, with the increase of damage, the resultant force direction inclines towards the wall's longitudinal direction regardless of the direction of the imposed displacement. Finally, recommendations are made for applicability of ASCE41‐06 formulations under different bidirectional loading conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Multi‐directional response of unreinforced masonry walls: experimental and computational investigations

This paper describes the results of an experimental and numerical study that focused on multi‐directional behavior of unreinforced masonry walls and established the requisite of the related proposed design equations. The tests were conducted following several sets of multi‐directional loading combinations imposed on the top plane of the wall along with considering monotonic and cyclic quasi‐static loading protocols. Various boundary conditions, representing possible wall–roof connections, were also considered for different walls to investigate the influence of rotation of the top plane of the wall on the failure modes. The results of the tests were recorded with a host of high precision data acquisition systems, showing three‐dimensional displacements of a grid on the surface of the wall. Finite element models of the walls are developed using the commercial software package ABAQUS/Explicit compiled with a FORTRAN subroutine (VUMAT) written by the authors. The experimental results were then used to validate the finite element models and the developed user‐defined material models. With the utility of validated models, a parametric study was performed on a set of parameters with dominant influence on the behavior of the wall system under in‐plane and out‐of‐plane loading combinations. The experimental and numerical results are finally used to investigate the adequacy of ASCE 41 empirical equations, and some insights and recommendations are made. Copyright © 2016 John Wiley & Sons, Ltd.     

The effective stiffness of modern unreinforced masonry walls

Code design of unreinforced masonry (URM) buildings is based on elastic analysis, which requires as input parameter the effective stiffness of URM walls. Eurocode estimates the effective stiffness as 50% of the gross sectional elastic stiffness, but comparisons with experimental results have shown that this may not yield accurate predictions. In this paper, 79 shear‐compression tests of modern URM walls of different masonry typologies from the literature are investigated. It shows that both the initial and the effective stiffness increase with increasing axial load ratio and that the effective‐to‐initial stiffness ratios are approximately 75% rather than the stipulated 50%. An empirical relationship that estimates the E‐modulus as a function of the axial load and the masonry compressive strength is proposed, yielding better estimates of the elastic modulus than the provision in Eurocode 6, which calculates the E‐modulus as a multiple of the compressive strength. For computing the ratio of the effective to initial stiffness, a mechanics‐based formulation is built on a recently developed analytical model for the force‐displacement response of URM walls. The model attributes the loss in stiffness to diagonal cracking and brick crushing, both of which are taken into account using mechanical considerations. The obtained results of the effective‐to‐initial stiffness ratio agree well with the test data. A sensitivity analysis using the validated model shows that the ratio of effective‐to‐initial stiffness is for most axial load ratios and wall geometries around 75%. Therefore, a modification of the fixed ratio of effective‐to‐initial stiffness from 50% to 75% is suggested.     

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.     

Seismic capacity of irregular unreinforced masonry walls with openings

Masonry buildings are often characterized by geometric irregularities. In many cases, such buildings meet global regularity requirements provided by seismic codes, but they are composed by irregular walls with openings. The latter are masonry walls characterized by (i) openings of different sizes, (ii) openings misaligned in the horizontal and/or vertical direction, or (iii) a variable number of openings per story. An irregular layout of openings can induce not only a nonuniform distribution of gravity loads among masonry piers but also unfavorable damage localizations resulting in a premature collapse of the wall and hence a higher seismic vulnerability. This paper is aimed at providing a simplified methodology to assess the effects of irregularities on the in‐plane seismic capacity of unreinforced masonry (URM) walls with openings. To this end, a macroelement method was developed and validated through experimental results available in the literature. The proposed methodology was based on the quantification of wall irregularities by means of geometric indices and their effects on seismic capacity of URM walls with openings through both sensitivity and regression analyses. Sensitivity analysis was based on a high number of static pushover analyses and allowed to assess variations in key seismic capacity parameters. Regression analysis let to describe each capacity parameter under varying irregularity index, providing empirical models for seismic assessment of irregular URM walls with openings. The in‐plane seismic capacity was found to be significantly affected by wall irregularities, especially in the case of openings with different heights. Copyright © 2012 John Wiley & Sons, Ltd.     

Out‐of‐plane strength reduction of unreinforced masonry walls because of in‐plane damages

There are numerous studies on the behavior of Unreinforced Masonry (URM) walls in both in‐plane (IP) and out‐of‐plane (OP) directions; however, few aimed at understanding the simultaneous contribution of these intrinsic responses during earthquakes. Undoubtedly, even a strong URM wall shows weakened capacity in the OP direction because of minor cracks and other damages in the IP direction, and this capacity reduction has not yet been accounted for in seismic codes. In this study, performance of three URM walls is evaluated by several numerical analyses in terms of the OP capacity reduction because of IP displacements and failure modes. Several parameters influencing the OP capacity have been studied including aspect ratio, roof boundary condition, IP displacement and IP loading patterns. The results indicate that reduction in the OP capacity of URM walls varies from negligible to very high depending on boundary conditions, IP failure mode and IP damage severity. Moreover, IP loading pattern is more important in walls with higher aspect ratios because of their IP failure modes. Copyright © 2015 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.     

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.     

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.     

Analytical and empirical models for predicting the drift capacity of modern unreinforced masonry walls

Displacement‐based seismic assessment of buildings containing unreinforced masonry (URM) walls requires as input, among others, estimates of the in‐plane drift capacity at the considered limit states. Current codes assess the drift capacity of URM walls by means of empirical models with most codes relating the drift capacity to the failure mode and wall slenderness. Comparisons with experimental results show that such relationships result in large scatter and usually do not provide satisfactory predictions. The objective of this paper is to determine trends in drift capacities of modern URM walls from 61 experimental tests and to investigate whether analytical models could lead to more reliable estimates of the displacement capacity than the currently used empirical models. A recently developed analytical model for the prediction of the ultimate drift capacity for both shear and flexure controlled URM walls is introduced and simplified into an equation that is suitable for code implementation. The approach follows the idea of plastic hinge models for reinforced concrete or steel structures. It explicitly considers the influence of crushing due to flexural or shear failure in URM walls and takes into account the effect of kinematic and static boundary conditions on the drift capacity. Finally, the performance of the analytical model is benchmarked against the test data and other empirical formulations. It shows that it yields significantly better estimates than empirical models in current codes. The paper concludes with an investigation of the sensitivity of the ultimate drift capacity to the wall geometry, static, and kinematic boundary conditions.     

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.     

Numerical study on factors that influence the in‐plane drift capacity of unreinforced masonry walls

Displacement‐based assessment procedures require as input reliable estimates of the deformation capacity of all structural elements. For unreinforced masonry (URM) walls, current design codes specify the in‐plane deformation capacity as empirical equations of interstory drift. National codes differ with regard to the parameters that are considered in these empirical drift capacity equations, but the inhomogeneity of datasets on URM wall tests renders it difficult to validate the hypotheses with the currently available experimental data. This paper contributes to the future development of such empirical relationships by investigating the sensitivity of the drift capacity to the shear span, the aspect ratio, the axial load ratio, and the size of the wall. For this purpose, finite element models of URM walls are developed in Abaqus/Explicit and validated against a set of experimental results. The results show that the axial load ratio, the shear span, and the wall size are among the factors that influence the drift capacity the most. Empirical equations are mainly derived from test results on small walls, and the numerical results suggest that this can lead to a significant overestimation of the drift capacity for larger walls.     

Assessment of the dynamic response of unreinforced masonry structures using a macroelement modeling approach

The seismic performance of unreinforced masonry structures is strongly associated with the interaction between in‐plane and out‐of‐plane mechanisms. The seismic response of these structures has been thoroughly investigated by means of experimental testing, analytical procedures, and computational approaches. Within the framework of the numerical simulations, models based on the finite element method provide a good prediction of the seismic performance of unreinforced masonry structures. However, they usually require a high computational cost and advanced user expertise to define appropriate mechanical properties and to interpret the numerical results. Because of these limitations, simplified models for practical applications have been developed during the last decades. Despite this, a great number of these models focus mostly on the evaluation of the in‐plane response, assuming box (or integral) behavior of the structure. In this paper, a simplified macroelement modeling approach is used to simulate the seismic response of 2 masonry prototypes taking into consideration the combined in‐plane and out‐of‐plane action. The numerical investigations were performed in the static and dynamic fields by using pushover analyses and nonlinear dynamic analyses respectively. The latter is a novel implementation of a model previously developed for static analysis. The results obtained from this study are in good agreement with those provided by a detailed nonlinear continuum FE approach, demonstrating the applicability of this macroelement model with a significant reduction of the computational cost.     

Seismic performance of masonry walls retrofitted with steel reinforced grout

An innovative solution for the seismic protection of existing masonry structures is proposed and investigated through shake table tests on a natural scale wall assemblage. After a former test series carried out without reinforcement, the specimen was retrofitted using Steel Reinforced Grout. The strengthening system comprises horizontal strips of ultra‐high strength steel cords, externally bonded to the masonry with hydraulic lime mortar, and connectors to transversal walls, applied within the thickness of the plaster layer. In order to assess the seismic performance of the retrofitted wall, natural accelerograms were applied with increasing intensity up to failure. Test results provide a deep understanding of the effectiveness of mortar‐based composites for improving the out‐of‐plane seismic capacity of masonry walls, in comparison with traditional reinforcements with steel tie‐bars. The structural implications of the proposed solution in terms of dynamic properties and damage development under earthquake loads are also discussed.Copyright © 2015 John Wiley & Sons, Ltd.     

Performance of masonry enclosure walls: lessons learned from recent earthquakes

This paper discusses the issue of performance requirements and construction criteria for masonry enclosure and infill walls.Vertical building enclosures in European countries are very often constituted by non-load-bearing masonry walls, using horizontally perforated clay bricks.These walls are generally supported and confined by a reinforced concrete frame structure of columns and beams/slabs.Since these walls are commonly considered to be nonstructural elements and their influence on the structural response is ignored,their consideration in the design of structures as well as their connection to the adjacent structural elements is frequently negligent or insufficiently detailed.As a consequence,nonstructural elements,as for wall enclosures,are relatively sensitive to drift and acceleration demands when buildings are subjected to seismic actions. Many international standards and technical documents stress the need for design acceptability criteria for nonstructural elements,however they do not specifically indicate how to prevent collapse and severe cracking,and how to enhance the overall stability in the case of moderate to high seismic loading.Furthermore,a review of appropriate measures to improve enclosure wall performance and both in-plane and out-of-plane integrity under seismic actions is addressed.     

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.     

Force‐displacement model for solid confined masonry walls with shear‐dominated failure mode

This paper addresses the behavior of confined masonry walls with dominating shear failure mode in walls. For this purpose, failure modes of these walls are classified in details. For each failure mode, complete set of analytical‐based relations for deriving parameters related to backbone curves is introduced. Calibrated finite element analyses are utilized as a benchmark for verification of some of the assumptions. The results of the proposed relations are compared with those of several Iranian and non‐Iranian experimental data. Sensitivity analysis is performed in order to understand the effects of important behavioral characteristics of these walls. The results of this study indicate that the proposed relations can accurately simulate behavior of confined masonry walls with dominating shear failure mode regardless of the failure mode in the ties. Moreover, it is concluded that the detailing limitations given in the Iranian Seismic Code are rationally compatible with the behavioral characteristics of confided masonry walls. The results of this study in terms of backbone curves can be utilized as the complementary part to this code. Copyright © 2017 John Wiley & Sons, Ltd.