A linear mathematical model for the seismic inplane behaviour of brick masonry walls part 2: Determination of model parameters through optimization using experimental data

The parameters appearing in the mixture and effective modulus models proposed in Part 1 are determined through optimization by matching theoretical and experimental responses. The optimization analysis is performed in frequency space. The response quantities chosen to be matched are the complex frequency response functions (experimental and theoretical) relating the Fourier transforms of top and base accelerations of the wall. Computations in optimization analysis are carried out by introducing an object (error) function and minimizing it using the Gauss-Newton method. The results show that the mixture model is capable of predicting accurately the dynamic response of masonry walls up to a frequency which is well above the second modal frequency, whereas the effective modulus model describes the wall behaviour only up to the first modal frequency. Furthermore, it is shown that the mixture model is still valid when micro cracks, which may exist between the mortar and brick constituents, are present.     

A linear mathematical model for the seismic inplane behaviour of brick masonry walls part 1: Theoretical considerations

In this study two mathematical models are presented for the linear dynamic behaviour of masonry walls. The study is completed in three stages: experimental observations, selection of a mathematical model and the determination of model parameters through optimization analysis. In the present paper (Part 1) the theoretical analysis used in the development of the mathematical models is presented. Part 2 is devoted to the optimization analysis. Evaluation of the experimental data, which is described in detail in Part 2, indicates that the first two modal frequencies of the wall specimen are close to each other. This may be attributed, on physical grounds, to strong interaction between the brick and mortar phases of the wall. Accordingly, a two-phase mathematical model, namely a mixture model (MM), is chosen to describe the wall behaviour because it can differentiate between the two phases of the wall and take into account the interaction between them. The equations of MM are put into a discrete form to simplify the optimization analysis. As a special case, MM contains a simple one-phase model called the effective modulus model (EMM). The equations of EMM are also established. Finally, the theoretical complex frequency response functions (CFRF) predicted by MM and EMM are obtained. CFRF relates the top acceleration of the wall to its base acceleration and is the response quantity chosen to be matched in the optimization analysis.     

The non-linear response of unreinforced masonry buildings to earthquake excitations

The three-dimensional non-linear earthquake behaviour of unreinforced masonry buildings is studied by using a constitutive model established experimentally for burned-clay brick masonry wall panels. The parameter functions appearing in the constitutive model are modified so that they accommodate a wall panel made of a general masonry material. In the study it is assumed that the floors of the masonry building are reinforced concrete slabs which are infinitely rigid in their own planes and that the wall panels possess only in-plane rigidities. Some examples involving earthquake analyses of two different masonry structures are presented. It is found that the predictions of the model used in the study are in harmony with the experimental data available in the literature.     

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。     

Review of strength models for masonry spandrels

Many older unreinforced masonry (URM) buildings feature timber floors and solid brick masonry. Simple equivalent frame models can help predicting the expected failure mechanism and estimating the strength of a URM wall. When modelling a URM wall with an equivalent frame model rather than, for example, a more detailed simplified micro-model, the strengths of the piers and spandrels need to be estimated from mechanical or empirical models. Such models are readily available for URM piers, which have been tested in many different configurations. On the contrary, only few models for spandrel strength have been developed. This paper reviews these models, discusses their merits, faults and compares the predicted strength values to the results of recent experimental tests on masonry spandrels. Based on this assessment, the paper outlines recommendations for a new set of strength equations for masonry spandrels.     

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.     

Seismic behaviour of confined masonry walls

The results of tests of plain and confined masonry walls with h/l ratio equal to 1·5, made at 1:5 scale, have been used to develop a rational method for modelling the seismic behaviour of confined masonry walls. A trilinear model of lateral resistance–displacement envelope curve has been proposed, where the resistance is calculated as a combination of the shear resistance of the plain masonry wall panel and dowel effect of the tie-columns’ reinforcement. Lateral stiffness, however, is modelled as a function of the initial effective stiffness and damage, occurring to the panel at characteristic limit states. Good correlation between the predicted and experimental envelopes has been obtained in the particular case studied. The method has been also verified for the case of prototype confined masonry walls with h/l ratio equal to 1·0. Good correlation between the predicted and experimental values of lateral resistance indicates the general validity of the proposed method. © 1997 John Wiley & Sons, Ltd.     

基于损伤塑性模型的砌体墙体非线性有限元分析

为了研究砌体墙体用钢结构加固后的力学性能,需要提供较准确的砌体墙体非线性计算,考虑到砌体与混凝土的材料性质具有相似性,将混凝土损伤塑性模型经修正后应用于砌体数值模拟,实现对砌体墙体的非线性有限元分析。通过与水平加载试验结果对比,验证了有限元模型的正确性。探讨了损伤塑性模型中的粘性系数、膨胀角、砌体本构关系中的初始弹性模量、受拉应力应变关系对计算结果的影响。结果表明：粘性系数和膨胀角对抗剪承载力、峰值位移及下降段性能均有较大影响,而对初始刚度影响很小;随着初始弹性模量的增大,砌体墙体抗剪承载力随之提高,但峰值位移无明显变化;受拉应力应变方程中待定系数的取值,对抗剪承载力及峰值位移影响较大。     

基于等效框架模型的砌体结构抗震模拟及验证

等效框架模型采用宏观模型来模拟砌体墙在平面内的抗震性能。砌体墙的墙柱和墙梁采用同时考虑轴向弯曲和剪切变形的基于力法的纤维截面进行模拟,且两者的连接视为刚性区域。轴向压缩及弯曲效应在截面纤维模型中考虑,而剪切效应由V-γ剪切恢复力模型表达,弯曲和剪切在单元层面进行耦合。通过统计和分析,确定骨架曲线的计算方法,并基于Ibarra-Krawinkler模型提出剪切恢复力模型。通过算例得出:该模型在单调加载和循环加载下的数值计算结果与试验结果均吻合较好。     

邀山阁游客流量控制研究

邀山阁是一座4层砖石结构楼阁,目前西北角墙体倾斜严重且墙体、石柱存在竖向裂缝。基于保护邀山阁的需要,应用等效体积单元（RVE）进行墙体的有限元分析,通过调整弹性模量和优化有限元模型来模拟砌体带裂缝时的工作状态;在应力值及其变化值比较大的关键部位选取了26个控制点,进行应力包络分析;在合理的安全系数和游客荷载最不利工况下,得到了邀山阁游客的合理控制数量。本研究将有益于古建筑的长期保护和合理开发利用。     

门窗间砌体墙抗震性能试验及转动变形机理分析

砌体墙弹性计算采用的无转动假定与砌体房屋震害中所表现的墙体破坏模式不完全相符,砌体墙的转动变形是墙体受力过程中总变形的重要组成部分,转动失效也是一种典型的破坏模式。在前期试验研究基础上,进行了3片足尺门窗间砌体墙试件的低周反复荷载试验,立面形状为“凸”形和“L”形,介绍了试件的破坏过程及转动现象,分析了试件的滞回曲线和承载力差异;探讨了门窗间砌体窗间墙的转动变形机理,并分析了材料强度、竖向荷载和立面形状等因素对砌体墙转动变形的影响。研究结果表明:本文荷载及约束条件下,门窗间砌体墙试件均表现出明显的转动失效特征,属于窗间墙转动或窗间墙连带窗下墙整体转动失效的破坏模式;砌体墙发生受剪破坏或转动失效的关键在于窗间墙水平截面的受剪能力是否大于其受到的水平荷载;砌体材料强度越高、高宽比越大和立面对称性越差,砌体墙越容易出现转动变形现象以及发生转动失效,反之则容易发生受剪破坏。本文试验以及研究内容关注了门窗间砌体墙在受力全过程中实际存在而又常常被忽略的转动变形问题,试验数据及研究结论可为更加深入地了解砌体墙的变形机制提供参考。     

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.     

地震作用下低层建筑砌体结构的动力特性分析

传统低层建筑砌体结构动力特性分析中,易受到外界环境的干扰,砌体结构的完整性欠缺,导致动力特性分析的准确度较低。为提高低层建筑砌体结构的抗震性能,提出地震作用下低层建筑砌体结构的动力特性分析方法。首先利用低层建筑砌体结构反应自功率谱,完成砌体结构的自振频率辨认;然后通过941B型超低频率测振仪测试自振频率,筛出振动波形中噪声干扰的区域,获取时域波形和频域波形;最后依据时域波形和频域波形塑造低层建筑砌体三维精细化模型,在该模型基础上,通过子空间迭代算法获取低层建筑砌体结构的模拟结果,分析地震作用下芯柱、圈梁等构造措施对建筑砌体结构动力特征的影响,完成砌体结构的动力特性分析。实验结果表明,利用所提方法对地震作用下低层建筑砌体结构的动力特性进行分析,得到的分析结果准确度较高。     

基于试验数据的砌体填充墙易损性研究

本文对砌体填充墙的损伤状态进行了划分,并将损伤状态与常用修复方案相关联,明确了不同损伤状态所需要的修复方案。为了建立适用于中国砌体填充墙的易损性函数,对砌体填充墙面内抗震性能的试验数据进行了统计分析以建立损伤状态与工程需求参数的拟合经验关系。以层间位移角作为填充墙的工程需求参数,通过对数正态分布拟合试验数据。结果表明采用对数正态分布拟合的易损性曲线能够满足Lilliefors检验要求,可将其用于砌体填充墙的易损性评估中。     

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

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

The relevance of energy damping in unreinforced masonry rocking mechanisms. Experimental and analytic investigations

Existing unreinforced masonry buildings frequently suffer out-of-plane local collapse mechanisms when undergoing earthquake ground motion. The energy damping that occurs during the motion, due to impacts of a wall against the foundation or against other walls, is a relevant parameter on the response. An experimental investigation has been carried out to estimate the dissipation of kinetic energy that takes place during free oscillations. Restraint conditions allow for two-sided rocking (wall resting on a foundation) and one-sided rocking (wall resting on a foundation adjacent to transverse walls). Five specimens have been tested, modelling walls acted out-of-plane (fa?ades). When one-sided rocking is under consideration, different depths of the contact surface between fa?ade and transverse walls are considered. In the case of two-sided rocking, the experimental coefficient of restitution is slightly lower than the analytic coefficient. In the case of one-sided rocking, an analytic formulation is proposed and this is compared against experimental data. Although the coefficient of restitution of one-sided rocking is less than half that of two-sided rocking, it is not equal to zero. Thus, it cannot induce a sudden stop of the motion. Hence, nonlinear time history analyses performed under this assumption may prove unsafe. Moreover, a comparison has been carried out between overturning maps, induced by twenty natural accelerograms, computed for the analytic coefficient of restitution and those computed for the experimental coefficient of restitution. The increased energy dissipation reduces the frequency of overturning and causes a more regular behaviour.     

新安江模型参数全局优化——以月潭流域为例

采用全局优化算法SCE-UA,以月潭流域为例对新安江模型参数优化进行研究.结果表明:采用理想资料时,SCEUA算法可以搜索到稳定的最优参数组;采用实际水文资料时,该算法不能保证得到唯一和稳定的最优参数组;对模型优化的目标函数进行探讨,发现对于新安江日模型,目标函数选取水量平衡误差函数或确定性系数函数较好,对于次洪模型选...     

Shake table testing of un‐reinforced brick masonry building test model isolated by U‐FREI

This paper presents a detailed study on feasibility of un‐bonded fiber reinforced elastomeric isolator (U‐FREI) as an alternative to steel reinforced elastomeric isolator (SREI) for seismic isolation of un‐reinforced masonry buildings. Un‐reinforced masonry buildings are inherently vulnerable under seismic excitation, and U‐FREIs are used for seismic isolation of such buildings in the present study. Shake table testing of a base isolated two storey un‐reinforced masonry building model subjected to four prescribed input excitations is carried out to ascertain its effectiveness in controlling seismic response. To compare the performance of U‐FREI, same building is placed directly on the shake table without isolator, and fixed base (FB) condition is simulated by restraining the base of the building with the shake table. Dynamic response characteristic of base isolated (BI) masonry building subjected to different intensities of input earthquakes is compared with the response of the same building without base isolation system. Acceleration response amplification and peak response values of test model with and without base isolation system are compared for different intensities of table acceleration. Distribution of shear forces and moment along the height of the structure and response time histories indicates significant reduction of dynamic responses of the structure with U‐FREI system. This study clearly demonstrates the improved seismic performance of un‐reinforced masonry building model supported on U‐FREIs under the action of considered ground motions. 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.