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.     

In-plane shear behaviour of unreinforced and jacketed brick masonry walls

This paper deals with the results of cyclic load tests on masonry walls performed for the purpose of evaluation of in-plane shear behaviour and identification of shear strength, stiffness and energy dissipation. Eight walls in two series were assembled in laboratory conditions. The first series consisted of four unreinforced masonry walls constructed from solid clay bricks and lime mortar. The walls from the second series were strengthened by application of RC jackets on both sides. These were constructed of the same material and were characterized by the same geometry properties and vertical load levels as those of the walls from the first series. The main goal of the tests was to compare the behaviour of the unreinforced and strengthened walls under cyclic horizontal load. The results from the tests showed that the application of the strengthening method contributed to a significant improvement of the shear resistance of the jacketed walls. Analytical models were used to predict the shear resistance of the walls. Good agreement with the experimental results was obtained with a model based on tensile strength of masonry.     

砌体结构抗震抗剪强度分析

进行了墙体抗剪强度理论和公式的研究。将主拉强度理论与剪摩强理论相结合,形成了一种新和强度理论,即拉摩强度理论。根据该理论,导出了墙体抗剪强度公式。给出了公式系数的确定方法,并确定了砖墙体的公式系数。将本文建议的砖墙体抗剪强度公式与抗震和砌体规范采用的抗剪强度公式进行了比较,比较结果表明：抗震规范公式值较小;砌体规范公式值较在,本文公式值介于两者中间。     

Seismic performance of an unreinforced masonry building: An experimental investigation

This paper presents the results of an experimental investigation carried out to investigate the seismic performance of a two storey brick masonry house with one room in each floor. A half‐scale building constructed using single wythe clay brick masonry laid in cement sand mortar and a conventional timber floor and timber roof clad with clay tiles was tested under earthquake ground motions on a shaking table, first in the longitudinal direction and then in the transverse direction. In each direction, the building was subjected to different ground motions with gradually increasing intensity. Dynamic properties of the system were assessed through white‐noise tests after each ground motion. The building suffered increasing levels of damage as the excitations became more severe. The damage ranged from cracking to global/local rocking of different piers and partial out‐of‐plane failure of the walls. Nevertheless, the building did not collapse under base excitations with peak ground acceleration up to 0.8g. General behaviour of the tested building model during the tests is discussed, and fragility curves are developed for unreinforced masonry buildings based on the experimental results. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Observed failure modes of unreinforced masonry buildings during the 2015 Hindu Kush earthquake

On 26 th October 2015, an Mw 7.5 earthquake struck northern Pakistan, with its epicenter located 45 km southwest of Jarm in the Hindu Kush region of Afghanistan. The earthquake resulted from reverse faulting at a depth of 210 km, resulting in 280 fatalities and substantial damage to some 109,123 buildings. Regional seismicity, characteristics of recorded strong motions, damage statistics, and building performance observations are presented. Earthquake damage was mostly constrained to seismic-deficient unreinforced masonry(URM) buildings. Typical failure modes included toppled minarets, partial or complete out of plane collapse of URM walls, diagonal shear cracking in piers, flexural cracking in spandrels, corner damage, pounding damage, and damage due to ground settlement. The majority of human loss resulted due to failure of URM walls and subsequent roof collapse. URM buildings located in rural hilly areas closer to the epicenter suffered more intense and frequent damage than urban URM buildings located farther away in larger cities.     

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.     

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.     

低屈服钢造耐震间柱构架之抗震行为

传统抗弯构架加入耐震间柱后可使刚度、强度与韧性获得提升,因此可设计为新建筑的抗震系统或既有建筑的补强.本文探讨一种中间段以低屈服强度钢材为腹板,高强度钢为翼板,上下段皆以高强度钢制成之三段式剪力屈服型耐震间柱.本文并使用非线性分析程序探讨耐震间柱的受震反应,并与一般抗弯构架作比较.由分析中可发现,楼层位移角及侧向位移均有显著的减小,其塑铰也由梁端成功地转移至间柱上.而耐震间柱的确也肩负起消能的责任,使得在地震发生时能消释构架中大部分的迟滞能量.     

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.     

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.     

A mathematical model for the in-plane non-linear earthquake behaviour of unreinforced masonry walls. Part 2: Completion of the model

In this part, the parameter functions for clay brick masonry appearing in the non-linear model are established for the wall material used in the experiments by means of experimental data and a particular type of optimization. This special optimization makes use of the fact that the wall behaves linearly at the intensity level of each excitation, as described in Part 1, and involves matching in frequency space the experimental and theoretical complex frequency response functions relating the Fourier transforms of the top and base accelerations of the wall. It is found that the envelope curves for the parameter functions are bilinear and that the dynamic values of mechanical properties of masonry differ greatly from their static values. The completed model is appraised by comparing how the wall will respond to strong earthquake excitations when predicted using the model and how it actually responded on the shaking table. The predicted response is remarkably close to the experimental.     

A database of the structural behavior of masonry in shear

This paper reports the results of several on-site investigations carried out by the authors in the last 20 years in central Italy (Umbria, Marche, Emilia and Abruzzo regions) on masonry wall panels. The use of stone and brickwork masonry has been common for centuries not only for rural residences but also for public and religious buildings. In many areas, where the stone was abundant, stone became the material of choice for all constructions. However from rubble stone to perfectly squared stones, the mechanical properties may highly differ. Test results are reported with an accurate survey and analysis of the masonry typology and mechanical characterization was performed according to ASTM standards and consisted of measurements of shear properties. The paper also reports the experimental results of full-scale tests conducted on brickwork walls using different bonding patterns, mortar types and brick dimensions. These data were recorded in terms of shear strength, elastic properties and deformation capacity and are of critical importance for design, reinforcement or retrofit purposes in earthquake-prone areas. All tests were conducted on site from pre-existing undamaged wall panels. Finally, test results are compared with existing standards and indicate that masonry shear strength is sometimes overestimated by the Italian Building Code.     

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.     

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.