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.     

土坯墙体抗震加固的试验研究

通过对4片西北地区传统土坯墙体在低周往复荷载作用下的抗震性能试验研究,对比分析了竹胶板及木柱木梁加固墙片的破坏形态、水平承载力、变形性能、骨架曲线、刚度退化曲线、滞回曲线与耗能性能。试验研究表明:加固墙片可有效提高墙体的抗震性能。在此基础上提出用竹胶板加固既有且在用的村镇土坯墙体房屋,该加固方式经济有效,又能在一定程度上保存建筑原始风貌,满足实际工程的设计要求。     

双层打包带加固窗间墙抗震性能试验研究

地震时砌体结构窗间墙易发生破坏,为了提高其抗震性能,对高宽比为1的2组共4片墙体,其中:2片为双层打包带加固墙体,2片为原墙,进行了拟静力试验,研究墙体的破坏形态、水平承载力、滞回曲线和耗能等抗震性能。试验发现原墙发生剪切破坏,加固后墙体发生摇摆破坏,加固改变了墙体破坏模式,加固后墙体滞回曲线饱满但有捏笼,破坏荷载、延性和耗能能力都有提高,破坏时未发生剥离,表明双层打包带加固法有效地提高了窗间墙体抗震性能,对承受较大竖向应力墙体效果更好,建议加固时要加强加固层与窗下和窗上墙体的连接。     

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.     

Seismic shear distribution among interconnected cantilever walls of different lengths

Mid‐rise to high‐rise buildings in seismic areas are often braced by slender reinforced concrete (RC) walls, which are interconnected by RC floor diaphragms. In design, it is typically assumed that the lateral forces are distributed in proportion to the wall's elastic stiffness. Pushover analyses of systems comprising walls of different lengths have, however, shown that large compatibility forces can develop between them, which should be considered in design, but the analyses have also shown that the magnitude of the computed forces is very sensitive to the modelling assumptions. Using the results of a complex shell element model as benchmark, different simple hand‐calculation methods and inelastic beam element models are assessed and improved to yield reliable estimates of the base shear distribution among the individual walls comprising the interconnected wall system. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

型钢混凝土剪力墙抗震性能影响参数研究

型钢混凝土剪力墙是一种广泛应用于高层混合结构中的剪力墙形式。本文采用通用有限元程序ADINA,以边缘构件含钢率为主要参数,对不同剪跨比的几组剪力墙承载力和变形能力进行了分析,并与考虑了剪力墙混凝土等级、轴压比、配筋率和边缘约束指标等参数影响的剪力墙性能进行了比较研究。结果表明,在高层结构中采用较高强度的混凝土是有利的,但剪力墙的轴压比需要严格限制,且墙体配筋率并不是提高其抗震性能的有效手段。在高层混合结构剪力墙中,通过边缘构件设置型钢可有效增加墙体延性,且边缘约束构件的约束指标可取0.32左右。     

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.     

Evaluation of active and passive seismic earth pressures considering internal friction and cohesion

The Log-Spiral-Rankine (LSR) model, which is a generalized formulation for assessing the active and passive seismic earth pressures considering the internal friction and cohesion of backfill soil, is reviewed and improved in this study. System inconsistencies in the LSR model are identified, which result from an inaccurate assumption on the vertical normal stress field (σ_z=γz) in a general c–ϕ soil medium, and from omitting the effect of soil cohesion when solving for the stress states along the failure surface. The remedies to the said inconsistencies are presented, and local and global iteration schemes are introduced to solve the resulting highly coupled multivariate nonlinear system of equations. The modified LSR model provides a more complete and accurate solution for earth retaining systems, including the geometry of the mobilized soil body, the stress state along the failure surface, as well as the magnitude and the point of application of the resultant earth thrust.     

Seismic stability analysis of gravity retaining walls

A new approach based on the category of upper bound theorem of limit analysis is presented in this study to consider the seismic stability of gravity retaining walls. The retaining wall and the backfill soil were taken as a whole system. For a translational failure mechanism assumed, formulas are provided to calculate directly the yield acceleration and the inclination of the failure surface. An example is shown to illustrate the method. Comparisons are made with limit equilibrium method, and the results are found consistent. Based on a limited parametric study, it is shown that the wall roughness has remarkable influence on the yield acceleration.