Abstract In this paper, we introduce an extension of the piecewise rigid displacement (PRD) method for addressing the stability of a generic two-dimensional masonry structure subjected to large displacements. So far, the PRD method has been applied to simulate cracks in the reference configuration considering small displacements. Here, we investigate both cracks and internal forces in the presence of large foundation displacements, also providing an approach to estimate their maximum allowable value. The proposed extension allows accounting for the evolution of both mechanism and corresponding internal stress state due to the increasing prescribed displacements. After benchmarking the PRD analysis of a pointed arch with a physical test and results obtained through the Discrete Element Modelling software 3DEC, its strength/use is demonstrated on a complex numerical application, based on the cross-section of a Gothic cathedral. Also in this case, the PRD results are compared with a 3DEC analysis showing good agreement in terms of cracks evolution, internal stress states and displacement capacity. This paper shows the ability of the PRD method in solving in a few seconds a critical issue in the field of masonry structures that is, the effects of large foundation displacements, both in terms of mechanisms and forces, simultaneously.

中文翻译：

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基于数值极限分析的砌体结构大位移建模

摘要 在本文中，我们介绍了分段刚性位移 (PRD) 方法的扩展，用于解决一般二维砌体结构在大位移下的稳定性问题。到目前为止，PRD 方法已应用于模拟考虑小位移的参考配置中的裂纹。在这里，我们研究了存在大地基位移时的裂缝和内力，还提供了一种估计它们的最大允许值的方法。拟议的扩展允许解释由于增加的规定位移而导致的机制和相应的内部应力状态的演变。在用物理测试和通过离散元建模软件 3DEC 获得的结果对尖拱的 PRD 分析进行基准测试后，基于哥特式大教堂的横截面，它的强度/用途在复杂的数值应用程序中得到了证明。同样在这种情况下，将 PRD 结果与 3DEC 分析进行比较，显示在裂纹演化、内应力状态和位移能力方面具有良好的一致性。本文展示了 PRD 方法在几秒钟内解决砌体结构领域的一个关键问题的能力，即大基础位移的影响，在机制和力方面，同时。