A nonlinear macroelement model for the seismic analysis of masonry buildings

The macroelement technique for modelling the nonlinear response of masonry panels is particularly efficient and suitable for the analysis of the seismic behaviour of complex walls and buildings. The paper presents a macroelement model specifically developed for simulating the cyclic in‐plane response of masonry walls, with possible applications in nonlinear static and dynamic analysis of masonry structures. The model, starting from a previously developed macroelement model, has been refined in the representation of flexural–rocking and shear damage modes, and it is capable of fairly simulating the experimental response of cyclic tests performed on masonry piers. By means of two internal degrees of freedom, the two‐node macroelement permits to represent the coupling of axial and flexural response as well as the interaction of shear and flexural damage. Copyright © 2013 John Wiley & Sons, Ltd.     

配筋砌体结构墙体出平面反应试验研究

为研究配筋砌体结构出平面反应,将配筋砌块未注芯的孔灌注了高密度铁砂,以提高缩尺模型材料的等效密度,更真实地模拟墙体出平面惯性效应.利用推导的模型与原型的相似关系,设计并实施了振动台试验.结果表明,模型结构主要以压弯变形为主,在现行规范规定的构造措施下,足以抵抗设防地震造成的墙体出平面破坏.通过敲击试验得到墙体出平面振动频率,该频率相对较高,远离地震动卓越频率.相邻楼层出平面频率不完全相同,振动的相位可能时而同相,时而反相.     

Evaluation of force-based and displacement-based out-of-plane seismic assessment methods for unreinforced masonry walls through refined model simulations

The performance of force-based and displacement-based seismic assessment methods for the life-safety limit state check of out-of-plane loaded unreinforced masonry walls is evaluated on the basis of refined numerical simulations. For this purpose, a discrete element model of a vertically spanning wall is built and validated against experimental results from static and dynamic test conditions. The model is then analysed for a large range of wall configurations. For each configuration, a static pushover analysis and a series of incremental dynamic analyses are run, the latter permitting to determine the capacity of the wall under dynamic loading. The accuracy of the assessment methods in predicting the acceleration at which the walls collapse is evaluated. It is found that the displacement-based method is more accurate, robust, and safe than the force-based method. The comparison also shows that for walls characterised by a relatively high ratio of axial load to Euler's critical load, both assessment methods lead to an overestimation of the wall capacity. As a remedy, a modification to the methods based on a recently developed mechanical model is put forward and tested. For the force-based method, it is additionally suggested to set for walls with relatively high overburden ratios the behaviour factor equal to 1. To ensure reproducibility of this study, all input and output files of the numerical simulations are made publicly available.     

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.     

Distinct element modelling of the in-plane cyclic response of URM walls subjected to shear-compression

The in-plane capacity of unreinforced masonry (URM) elements may vary considerably depending on several factors, including boundary conditions, aspect ratio, vertical overburden, and masonry texture. Since the overall system resistance mainly relies on the in-plane lateral capacity of URM components when out-of-plane modes are adequately prevented, the structural assessment of URM structures could benefit from advanced numerical approaches able to account for these factors simultaneously. This paper aims at enhancing and optimising the employment of the distinct element method, currently confined to the analysis of local mechanisms of reduced-scale dry-joint blocky assemblies, with a view to simulate the experimentally observed responses of a series of URM full-scale specimens with mortared joints subjected to quasi-static in-plane cyclic loading. To this end, a mesoscale modelling approach is proposed that employs a simplified microscale modelling approach to effectively capture macroscale behaviour. Dynamic relaxation schemes are employed, in combination with time, size, and mass-scaling procedures, to decrease computational demand. A new methodology for numerically describing both unit, mortar and hybrid failure modes, also including masonry crushing due to high-compression stresses, is proposed. Empirical and homogenisation formulae for inferring the elastic properties of interface between elements are also verified, enabling the proposed approach to be applied more broadly. Using this modelling strategy, the interaction between stiffness degradation and energy dissipation rate was accounted for numerically. Although the models marginally underestimate the energy dissipation in the case of slender piers, a good agreement was obtained in terms of lateral strength, hysteretic response, and crack pattern.     

多层错层砖砌体房屋抗震分析

本文根据典型的东西和南北错层单元模型,按不同的错层高度、不同收层情况和不同理置深度的实际房屋情况,分析建立了错层房层和相应的等效规整房屋模型,采用板壳单元,用有限元方法计算了这些模型的动力特征和在地震作用下的墙肢剪应力分布,经过对比分析得到了一些错层房屋墙应力的分布规律。根据错层房屋的受力特点,文中提出了相应的加强构造措施,结构布置要求和错层房屋的抗震计算模型等具体建议。     

An integrated macroelement formulation for the dynamic response of inelastic deformable rocking bodies

This paper presents a macroelement formulation for the prediction of the planar dynamic response of inelastic deformable rocking bodies. The formulation is based on a previous macroelement developed by the authors able to describe the cyclic response of inelastic rocking bodies, which takes into account the deformability both along the height of the member, as well as near the rocking end. Modifications of this formulation to account for other motion modes of rocking members during their dynamic response, namely, sliding and upthrow, as well as modifications to account for damping in a uniform manner during the whole motion, including impacts, are introduced. The dynamic response predicted by the macroelement for free-standing rigid and deformable rocking bodies is presented and compared with existing theoretical solutions, and the effect of deformability, damping, inelasticity, and friction on the response is discussed.     

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.     

Pseudo‐dynamic seismic response of reinforced concrete frames infilled with non‐structural brick masonry

This paper presents pseudo‐dynamic test results on the in‐plane seismic behaviour of infilled frames. Thirteen single‐storey, single‐bay, half‐size‐scale, reinforced concrete‐frame specimens, most of which infilled with non‐structural masonry made of perforated bricks and cement mortar are tested. The infills are in contact with frames, without any connector; openings are not covered. The frames are different in their strength and details, reinforcement grade, and aspect ratio. Seismic input is the 1976 Tolmezzo (Friuli, Italy) ground acceleration, to which specimens are subjected two times: virgin and damaged by the previous test. The global seismic response of initially virgin infilled specimens considerably differs from that of bare specimens. This follows a dramatic change of properties: compared to a bare frame, the initial stiffness increases by one order of magnitude, and the peak strength more than doubles. The peak drift lessens; however, the displacement ductility demand does not. The energy demand is greater. Nevertheless, the influence of infill decreases as damage proceeds. Displacement time histories of damaged specimens are quite similar. At the local level, infill causes asymmetry and concentration of the frame deformation. Copyright © 2005 John Wiley & Sons, Ltd.     

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

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

竖向变刚度约束砌体结构抗震能力研究

汶川8.0级特大地震发生时,前山断裂从彭州市白鹿中学两栋教学楼中间穿过,断层距离两栋教学楼仅数米,造成前楼严重破坏,破坏现象非常典型。该结构为外廊式单跨约束砌体结构教学楼,抗震设防烈度为7度,承重墙体的构造特点有别于当地的普通砌体结构,本文采用现场测试、震害考察和弹塑性地震反应计算分析等手段对该结构的抗震性能进行了详细的研究,旨在揭示具有这类构造形式的砌体结构在不同烈度影响场下的破坏特点和抗震能力,为指导今后砌体结构的设计和抗震规范的修改提供参考。     

蒸压加气混凝土砌块砌体填充墙框架结构抗震性能试验

为进一步改善框架结构平面内和平面外抗震性能,本文提出带X形斜撑的新型砌体填充墙构造方案,并进行了4榀蒸压加气混凝土砌块砌体填充墙框架结构试验,以研究墙体构造措施和墙-框连接方式对框架结构抗震性能的影响。首先进行平面内水平低周往复荷载试验,随后进行历经平面内损伤的平面外单调静力加载试验,最后进行承载力、刚度退化和耗能能力等抗震性能指标的分析。结果表明:墙-框柔性连接方案下,填充墙框架结构的平面内及平面外水平承载力和初始刚度均小于刚性连接方案,而变形能力、耗能能力和位移延性等性能指标均比刚性连接表现更好;墙-框柔性连接且填充墙带X形斜撑框架结构的平面内及平面外抗震性能指标均有明显改善,更有利于抗震。     

A framework for the seismic assessment of existing masonry buildings accounting for different sources of uncertainty

The current formulation of Eurocode 8 Part 3 and the Italian building code for the seismic assessment of existing buildings accounts for epistemic (knowledge‐based) uncertainties by means of the identification of knowledge levels with associated values of the so‐called confidence factors, applied only as a reduction of material strengths. This formulation does not always produce consistent results and it does not explicitly account for other sources of uncertainty. The paper proposes a probabilistic methodology for the quantification of appropriately defined factors, allowing consideration of the different sources of uncertainty involved in the seismic assessment of masonry buildings by means of nonlinear static analyses. This simple approach, also including an alternative formulation of the confidence factors related with material properties, allows to obtain results which are consistent with the acquired level of knowledge and correctly account for the different sources of uncertainty without requiring to carry out any stochastic nonlinear analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

填充墙RC框架结构加固方法的研究现状及展望

综述了用于提高填充墙钢筋混凝土(RC)框架结构抗震性能和改善结构损伤模式的几类加固措施,从工艺、加固效果和破坏形式3个角度进行了分析.在建筑结构设计过程中,填充墙通常被视为一种典型的脆性非均质非结构构件,忽视了填充墙与RC框架之间的相互作用.地震调查报告表明,在结构遭受地震作用时,填充墙通常先于钢筋混凝土框架发生破坏,...     

Shake‐table tests of a three‐story reinforced concrete frame with masonry infill walls

This paper presents the shake‐table tests of a 2/3‐scale, three‐story, two‐bay, reinforced concrete frame infilled with unreinforced masonry walls. The specimen is representative of the construction practice in California in the 1920s. The reinforced concrete frame had nonductile reinforcement details and it was infilled with solid masonry walls in one bay and infill walls with window openings in the other bay. The structure was subjected to a sequence of dynamic tests including white‐noise base excitations and 14 scaled historical earthquake ground motion records of increasing intensity. The performance of the structure was satisfactory considering the seismic loads it was subjected to. The paper summarizes the design of the specimen and the major findings from the shake‐table tests, including the dynamic response, the load resistance, the evolution of damage, and the final failure mechanism. Copyright © 2011 John Wiley & Sons, Ltd.     

强震作用下砌体结构倒塌过程仿真分析

四川汶川地震中大量砌体房屋倒塌,造成巨大人员伤亡。为研究和预防砌体结构震害,本文概述了多层砌体房屋的主要震害特点,研究了砌体结构地震倒塌分析方法、失效单元与结构倒塌等关键技术问题。利用动力有限元程序LS-DYNA模拟了砌体结构的倒塌过程。仿真计算的结果与真实倒塌过程吻合较好,说明通过合理选取计算参数和计算模型,可以对这种特殊的复杂破坏过程进行模拟分析和仿真。通过再现倒塌过程,发现了结构在强震作用下的薄弱环节,为提高砌体结构抗震性能研究、建立结构防倒塌机制提供了有力的技术支撑。     

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.     

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.     

Shaking table tests and dynamic analyses of masonry wall buildings with frame-shear walls at lower stories

This paper describes shaking table tests of three eight-story building models： all are masonry structures in the upper stories, with or without frame-shear walls of one- or two- stories at the bottom. The test results of damage characteristics and seismic responses are provided and compared. Then, nonlinear response analyses are conducted to examine the reliability of the dynamic analysis. Finally, many nonlinear response analyses are performed and it is concluded that for relatively hard sites under a certain lateral stiffness ratio （i.e., the ratio of the stiffness of the lowest upper masonry story to that of the frame- shear wall story）, the masonry structure with one-story frame-shear wall at the bottom performs better than a structure built entirely of masonry, and a masonry structure with frame-shear wall of two stories performs better than with one-story frame- shear wall. In relatively soft soil conditions, all three structures have similar performane. In addition, some suggestions that could be helpful for design of masonry structures with ground story of frame-shear wall structure in seismic intensity region VII, such as the appropriate lateral stiffness ratio, shear force increase factor of the frame-shear wall story, and permissible maximum height of the building, are proposed.     

水泥砂浆面层加固砌体墙抗震可靠指标研究

采用水泥砂浆面层加固方法加固砌体房屋是一种简单有效的方法。对比分析了《砌体结构加固设计规范》(GB 50702-2011)^[3]和《建筑抗震加固技术规程》(JGJ 116-2009)^[4]中钢筋网水泥砂浆面层加固砌体墙的可靠性;对10片未加固低强度砖墙和20片单面钢筋网水泥砂浆面层加固低强度砖墙进行拟静力试验,分析了未加固和加固墙体的破坏模式和机理,并提出了适用于钢筋网水泥砂浆面层加固砌体墙的抗震验算公式。研究表明：两标准的可靠水平差别较大,实际应用时,易产生矛盾;未加固墙主要发生沿阶梯形斜裂缝受剪破坏,加固墙主要发生沿通缝受剪破坏和沿阶梯形斜裂缝受剪破坏;建议公式的计算值与试验值吻合良好,未加固墙抗震可靠指标为2.2,加固墙抗震可靠指标为2.5～3.1;砂浆面层加固砌体结构可以显著提高结构的抗震性能。