Collapse of masonry structures under the influence of seismic action typically takes place via specific failure mechanisms, which have been well-documented. Assuming these mechanisms can be modelled as a kinematic chain, equations of motion can be derived and solved to predict dynamic rocking response. Previous derivations typically assume that the kinematic chain is comprised of rigid bodies with rigid interfaces, which are assumptions that can be both unrealistic and un-conservative. In this paper, rocking equations of motion are re-derived considering the presence of flexible interfaces and crushing effects. Specifically, new derivations are presented for single, two and multiple block mechanisms, while two different formulations for modelling non-rigid interfaces are also proposed. These formulations are compared, and the importance of interface flexibility is evaluated through comparison of the new models with previous formulations that assume purely rigid interfaces. The new equations of motion are also practically evaluated through comparison with advanced numerical modelling simulations.

中文翻译：

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在多块砌体倒塌机制中考虑界面灵活性和破碎效应的方法

在地震作用的影响下砌体结构的倒塌通常是通过特定的失效机制发生的，这已被充分记录。假设这些机制可以建模为运动链，则可以推导出和求解运动方程以预测动态摇摆响应。先前的推导通常假设运动链由具有刚性界面的刚体组成，这些假设既不切实际又不保守。在本文中，考虑到柔性界面和破碎效应的存在，重新推导了摇摆运动方程。具体来说，提出了单块、双块和多块机制的新推导，同时还提出了两种不同的非刚性界面建模公式。比较这些配方，并且通过将新模型与假设纯刚性界面的先前公式进行比较来评估界面灵活性的重要性。新的运动方程也通过与先进的数值建模模拟进行比较来实际评估。