Critical state theory is widely accepted for understanding and interpreting the behavior of granular materials such as sandy soils. Recently, motivated by the development of a multiscale analysis method, this paper presents a discrete element investigation on the critical state behavior of granular materials on two scales level, that is, the macroscale and mesoscale. Loops are taken as the basic mesostructures, and the concept of mesoscale critical state is proposed on terms of the local stress and void ratio. Based on series of numerical simulations with varying densities and confining pressures, the characters of critical state lines (CSLs) for each loop type are analyzed. An analytical relationship of the transition from local to global is then obtained for critical state. Besides, the influence of interparticle friction coefficient on CSL is also discussed on both scales. The prominent observation is that each type of loops achieves its own critical state, from which a unique global CSL can be obtained. The CSLs of different loops exhibit same shapes but move upwards with the increasing order.

中文翻译：

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中尺度颗粒材料的临界状态：从本地到全球的过渡

临界状态理论被广泛接受，以理解和解释诸如沙土之类的颗粒状物质的行为。近年来，受多尺度分析方法发展的启发，本文对宏观和中尺度两个尺度的颗粒材料的临界状态行为进行了离散元素研究。以环为基本的介观结构，并根据局部应力和空隙率提出了介观临界状态的概念。基于一系列具有不同密度和围压的数值模拟，分析了每种回路类型的临界状态线（CSL）的特征。然后获得临界状态从局部到全局的转换关系。除了，两种尺度上都讨论了颗粒间摩擦系数对CSL的影响。突出的观察结果是，每种类型的循环都达到其自己的临界状态，从中可以获得唯一的全局CSL。不同回路的CSL呈现相同的形状，但随着顺序增加而向上移动。