The evolutions of meso structures of granular materials play important roles during shearing toward the critical state. This study aims to establish an extended analytical model based on a specific upscaling procedure considering the distributions of meso structures in granular materials. A general Gaussian distribution is applied when determining the relationship between meso critical state parameters and order n, and then a quantitative model of macro CSL is developed by taking the discrete case into a continuous function. The quantitative model is then related to interparticle friction μ and contact stiffness k for predicting the macro CSLs for ideal granular assemblies, and the analytical results have good agreement with DEM results. Furthermore, the influence patterns of contact properties on both meso and macro critical states are discussed in detail, which provides a roughly explanation on the variations of critical friction angle ${\phi }_{cs}$ with μ.

中文翻译：

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考虑颗粒材料中细观结构分布的放大临界状态

颗粒材料细观结构的演变在向临界状态剪切过程中起着重要作用。本研究旨在考虑颗粒材料中细观结构的分布，建立基于特定放大程序的扩展分析模型。在确定细观临界状态参数与阶数n之间的关系时，应用一般的高斯分布，然后通过将离散情况转化为连续函数来建立宏观 CSL 的定量模型。然后定量模型与粒子间摩擦μ和接触刚度k 相关用于预测理想颗粒组件的宏观 CSL，分析结果与 DEM 结果有很好的一致性。此外，详细讨论了接触特性对细观和宏观临界状态的影响模式，这对临界摩擦角的变化提供了粗略的解释${\phi }_{C秒}$与μ。