Abstract This paper presents a 3D model aiming at investigating the out-of-plane collapse behavior of multi-leaf non-periodic masonry walls. These structural elements are widely employed in several constructions that are part of the European architectural heritage, but have been seldom addressed in the available literature due to their natural complexity and uniqueness. Specifically, the model here proposed allows a quick assessment of the out-of-plane collapse behavior of multi-leaf walls through the extraction of out-of-plane homogenized failure surfaces, acting as macroscopic failure criteria in bending and torsion. These failure surfaces are obtained after solving a standard-form linear programming problem written into a MATLAB script, which expresses a limit analysis problem pairing the well-established upper bound theorem and a homogenization approach. A twofold numerical application is performed by investigating a rubble masonry three-leaf wall and a quasi-regular three-leaf wall; in the latter case study, the influence of the rate of transversal interconnection between the outer wythes of the wall is also investigated. The results show that the presence of two different masonry bonds in the outer wythes entails some changes in the out-of-plane collapse behavior of the two case studies: namely, the out-of-plane response of the wall both under flexural and torsional actions is increased for the rubble masonry three-leaf wall, whereas it is decreased for the quasi-regular three-leaf wall. Moreover, in the latter case it is once more confirmed that a good transversal interconnection between the outer wythes - usually brought by the presence of transversal bricks – has beneficial effects on its out-of-plane collapse behavior, which are displayed both by the out-of-plane homogenized failure surfaces and deformed shapes at collapse.

中文翻译：

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非周期性多叶砌体墙的 3D 均质化极限分析

摘要 本文提出了一个 3D 模型，旨在研究多叶非周期性砌体墙的平面外倒塌行为。这些结构元素广泛用于作为欧洲建筑遗产一部分的几种建筑中，但由于其自然的复杂性和独特性，很少在现有文献中提及。具体来说，这里提出的模型允许通过提取平面外均质破坏面，作为弯曲和扭转的宏观破坏标准，快速评估多叶墙的平面外倒塌行为。这些失效面是在解决写入 MATLAB 脚本的标准形式线性规划问题后获得的，它表达了一个极限分析问题，将完善的上限定理和同质化方法配对。通过研究碎石砌体三叶墙和准规则三叶墙进行双重数值应用；在后一个案例研究中，还研究了墙外墙之间横向互连率的影响。结果表明，外墙中存在两种不同的砌体键导致两个案例研究的平面外倒塌行为发生了一些变化：即，墙体在弯曲和扭转作用下的平面外响应碎石砌体三叶墙的作用增加，而准规则三叶墙的作用减少。而且，