Granular filters are used in hydraulic earthen structures as a natural barrier to protect base soils from erosion under seepage conditions. Their performance is greatly dependent on the pore space connectivity that provides transport pathways for migrating fine particles. Traditional filter design rules are based on characteristic particle diameters of the involved materials, which do not explicitly reflect the pore structure dimensions. Even though the literature offers some mathematical tools that can be used to characterize the opening size of granular filters, the underlying physical fundamentals are still not sufficiently understood. Therefore, this study aims to provide a plausible physical framework for determining the filter opening size by means of numerical simulations using the discrete element method. From the investigation of particle transport processes in polydisperse packings of spheres, the opening sizes associated to these numerical filters are defined on the basis of their constriction size distribution. A mathematical procedure is then introduced to determine the effective opening size of the filter and subsequently, a revised retention criterion for granular filters is proposed and validated with experimental data from the literature. The study findings can offer a valuable perspective for erosion assessment methods in both new and existing earthen structures.

中文翻译：

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颗粒过滤器开口尺寸的确定

颗粒过滤器在水工土结构中用作天然屏障，以保护基础土壤在渗流条件下免受侵蚀。它们的性能在很大程度上取决于为迁移细颗粒提供传输途径的孔隙空间连通性。传统的过滤器设计规则基于所涉及材料的特征粒径，并没有明确反映孔结构尺寸。尽管文献提供了一些可用于表征颗粒过滤器开口尺寸的数学工具，但潜在的物理基础仍然没有得到充分理解。因此，本研究旨在提供一个合理的物理框架，通过使用离散元方法的数值模拟来确定过滤器开口尺寸。通过对球体多分散填料中颗粒传输过程的研究，与这些数字过滤器相关的开口尺寸是根据它们的收缩尺寸分布来定义的。然后引入数学程序来确定过滤器的有效开口尺寸，随后，提出了改进的颗粒过滤器保留标准，并使用文献中的实验数据进行了验证。研究结果可以为新土结构和现有土结构的侵蚀评估方法提供有价值的观点。然后引入数学程序来确定过滤器的有效开口尺寸，随后，提出了改进的颗粒过滤器保留标准，并使用文献中的实验数据进行了验证。研究结果可以为新土结构和现有土结构的侵蚀评估方法提供有价值的观点。然后引入数学程序来确定过滤器的有效开口尺寸，随后，提出了改进的颗粒过滤器保留标准，并使用文献中的实验数据进行了验证。研究结果可以为新土结构和现有土结构的侵蚀评估方法提供有价值的观点。