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.     

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 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.     

墙体开洞影响下房屋砖砌体结构地震易损性分析

为获取可靠的墙体开洞影响下房屋砖砌体结构地震易损性分析结果,采用ABAQUS有限元分析软件构建房屋砖砌体结构墙体模型,设置合理的墙体模型参数和数值模拟参数;对比模拟数值与以往研究的测试值,证明所构建模型参数取值合理;将截取的峰值段江油地震波作为上述模型的地震动输入,根据测得的房屋砖砌体结构的力学变化数据,分析房屋砖砌体结构的地震易损性。分析结果表明:地震情况下,随着墙体开洞率的增加,墙体荷载能力下降、墙体水平承载力增长幅度降低、墙体相对刚度退化率增加;墙体开洞数量越多,房屋砖砌体结构侧向刚度下降越快。因此分析得出墙体开洞率大、墙体开洞数量多,房屋砖砌体结构的地震易损性越显著。     

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.     

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.     

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.     

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.     

Seismic vulnerability of roof systems combining URM gable walls and timber diaphragms

Typical low-rise masonry buildings consist of unreinforced masonry (URM) walls covered with various timber roof configurations generally supported or finished by masonry gables. Post-earthquake observations and experimental outcomes highlighted the large vulnerability of the URM gables to the development of overturning mechanisms, both because of the inertial out-of-plane excitation and the in-plane timber diaphragm deformability. This paper presents the static and dynamic experimental seismic performance of three full-scale roofs tested via quasi-static cyclic and shake table tests. Two of them were tested as part of a whole full scale one-storey and two-storey building. A single-degree-of-freedom (SDOF) numerical model is calibrated against experimental data and proposed for the analysis of this roof typology's dynamic behaviour. Several sets of analyses were conducted to assess the vulnerability of these structural components and to study the effect of the whole building's characteristics (eg, number of storeys and structural stiffness and strength) on the seismic performance of this roof typology.     

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.     

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.     

Effects of vertical irregularity and thickness of unreinforced masonry infill on the robustness of RC framed buildings

Presence of irregularities in reinforced concrete (RC) buildings increases seismic vulnerability. During severe seismic shaking, such buildings may suffer disproportionate damage or even collapse that can be minimized by increasing robustness. Robustness is a desirable property of structural systems that can mitigate susceptible buildings to disproportionate collapse. In this paper, the effects of vertical irregularity and thickness of unreinforced masonry infill on the robustness of a six‐story three‐bay RC frame are quantified. Nonlinear static analysis of the frame is performed, and parametric study is undertaken by considering two parameters: absence of masonry infill at different floors (i.e., vertical irregularities) and infill thickness. Robustness has been quantified in terms of stiffness, base shear, ductility, and energy dissipation capacity of the frame. It was observed that the infill thickness and vertical irregularity have significant influence on the response of RC frame. The response surface method is used to develop a predictive equation for robustness as a function of the two parameters. The predictive equation is validated further using 12 randomly selected computer simulations. Copyright © 2013 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.     

Nonlinear analysis of masonry structures using fiber-section line elements

For seismic analysis of unreinforced masonry (URM) buildings characterized by a box-like behavior, a widely accepted model is based on the equivalent frame idealization of walls. The equivalent frame model uses 1D elements to represent the vertical piers and horizontal spandrels which are connected by rigid nodes. The mechanical characterization of the elements is one of the crucial aspects to predict reasonably the building seismic behavior. Through the comparison with pseudo-static and dynamic experimental tests performed on two-story full-scale buildings, this paper validates the frame modeling in the OpenSees framework, which includes a fiber-section force-based beam element for the axial-flexural behavior, coupled with a cyclic shear-deformation phenomenological law.     

Application of an in-plane/out-of-plane interaction model for URM infill walls to dynamic seismic analysis of RC frame buildings

Experimental tests have shown that unreinforced masonry (URM) infill walls are affected by simultaneous loading in their in-plane and out-of-plane directions, but there have been few attempts to represent this interaction in nonlinear time history analysis of reinforced concrete (RC) buildings with URM infill walls. In this paper, a recently proposed macro-model that accounts for this interaction is applied to the seismic analysis of RC framed structures with URM infill walls representative of Mediterranean building stock and practices. Two RC framed structures that are representative of low and mid-rise residential buildings are analysed with a suite of a bidirectional ground motions, scaled to three different intensities. During the analyses, the in-plane/out-of-plane interaction is monitored, showing that cracking of the infills occurs predominantly by in-plane actions, while failure occurs due to a combination of in-plane and out-of-plane displacements, with the out-of-plane component usually playing the dominant role. Along the frame height, the bottom storeys are generally the most damaged, especially where thin infill walls are used. These results are consistent with observations of damage to URM infill walls in similar buildings during recent earthquakes.     

Implications of the spandrel type on the lateral behavior of unreinforced masonry walls

Seismic response of unreinforced masonry (URM) buildings is largely influenced by nonlinear behavior of spandrels, which provide coupling between piers under in‐plane lateral actions. Seismic codes do not appropriately address modeling and strength verification of spandrels, adapting procedures originally proposed for piers. Therefore, research on spandrels has received significant attention in some earthquake‐prone countries, such as Italy and New Zealand. In the last years, the authors of this paper have performed both monotonic and cyclic in‐plane lateral loading tests on full‐scale masonry walls with single opening and different spandrel types. Those tests were carried out in a static fashion and with displacement control. In this paper, experimental outcomes for two as‐built specimens are presented and compared with those obtained in the past for another as‐built specimen with a wooden lintel above the opening. In both newly tested specimens, the masonry above the opening was supported by a shallow masonry arch. In one of those specimens, a reinforced concrete (RC) bond beam was realized on top of the spandrel, resulting in a composite URM‐RC spandrel. Then, the influence of spandrel type is analyzed in terms of observed damage, force–drift curves, and their bilinear idealizations, which allowed to compare displacement ductility and overstrength of wall specimens. Furthermore, effects of rocking behavior of piers are identified, highlighting their relationship with hysteretic damping and residual drifts. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic fragility reduction of an unreinforced masonry school building through retrofit using ferrocement overlay

The Himalayan region is one of the major seismic areas in the world. However, similar to many other seismically active locations, there are substantial numbers of unreinforced masonry(URM) buildings; the majority of which have not been designed for seismic loads. Past seismic events have shown that such buildings are highly vulnerable to earthquakes. Retrofitting of these URM buildings is an important concern in earthquake mitigation programs. Most government school buildings in rural areas of northern India are constructed of unreinforced masonry. These school buildings are socially important structures and serve as a crucial resource for rehabilitation during any disaster. The effectiveness of ferrocement(FC) to create a URM-FC composite is described in this study by estimating the performance and fragility of a URM school building before and after a retrofit. Analytical models, based on the equivalent frame method, are developed and used for nonlinear static analysis to estimate the enhancement in capacity. The capacity enhancement due to retrofitting is presented in terms of the maximum PGA sustained and damage probabilities at the expected level of earthquake hazard.     

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.     

Advanced frame element for seismic analysis of masonry structures: model formulation and validation

This paper presents a masonry panel model for the nonlinear static and dynamic analysis of masonry buildings suitable for the seismic assessment of new and existing structures. The model is based on an equivalent frame idealization of the structure and stems from previous research on force‐based frame elements. The element formulation considers axial, bending, and shear deformations within the framework of the Timoshenko beam theory. A phenomenological cyclic section law that accounts for the shear panel response is coupled, through equilibrium between shear and bending forces along the element, with a fiber‐section model that accounts for the axial and bending responses. The proposed panel model traces with a low computational burden and numerical stability the main aspects of the structural behavior of masonry panels and is suitable for analyses of multi‐floor buildings with a relatively regular distribution of openings and with walls and floors organized to grant a box‐like behavior under seismic loads. The model capabilities are validated though analyses of simple unreinforced masonry panels and comparisons with published experimental results. The model accuracy is strongly dependent on the fiber and shear constitutive laws used. However, the formulation is general, and laws different from those employed in this study are easily introduced without affecting the model formulation. Copyright © 2015 John Wiley & Sons, Ltd.     

增设翼柱的底商多层砌体房屋抗震性能试验研究

为研究在结构前纵墙底层部位增设翼柱对底商多层砌体房屋抗倒塌性能的影响,分别设计了一个1/5缩尺比例的普通底商多层砌体房屋及增设翼柱的砌体房屋模型分别进行振动台试验研究,对比分析各模型的破坏过程、加速度放大系数、相对位移及典型位置应变等参数。结果表明,在同样的地震动输入下,带有翼柱的底商多层砌体房屋破坏程度、层间相对位移及层间位移角均明显低于普通底商多层砌体房屋,带有翼柱的底商多层砌体房屋抗倒塌性能显著提高。