Physical elucidation of the behaviors of sand-pile avalanches like self-organized criticality and like characteristic earthquakes

众所周知，沙堆实验中的雪崩行为可分为两类，一类是自组织临界性行为，另一类是特征类地震行为。这两种类型仅由沙子直径与在其上产生沙堆的圆盘的直径之比确定。这一事实已被许多实验所证实，但还没有给出令人满意的物理解释。这项研究的目的是阐明这一现象的潜在物理原因。我们关注沙堆内部的应力链结构。因此，我们对光弹性材料制成的二维沙堆进行了光弹性分析和离散单元法(DEM)的模拟。通过对实验和模拟结果的详细观察，提出了一种可能的雪崩机制：对于处于临界状态的沙堆，决定雪崩大小的可能是某种不均匀。当沙堆很小时，雪崩的大小很小，因为表面颗粒的不均匀分布可能是系统的主要不均匀。然而，当桩变大时，桩的深处会被收紧和固结，而靠近地面的部分永远不会因为反复的雪崩而收紧。强度上的反差成为造成不均匀的主要因素。

It is known that the behavior of avalanches in sandpile experiments is categorized into two types; one is the self-organized criticality like behavior, and another is the characteristic earthquake like behavior. These two types are determined solely by the ratio of sand diameter to the diameter of the disk on which the sandpile is created. This fact has been confirmed by a number of experiments, but the satisfactory physical explanation has not been given. The purpose of this study is to clarify the underlying physics of this phenomenon. We focus on the stress chain structure inside a sandpile. So we use a photo-elastic analysis of two-dimensional sandpile made of photo-elastic material and a simulation by discrete element method(DEM).A detailed observation of the results of the experiment and the simulation suggests a possible mechanism of avalanches: for a sandpile in a critical state, what determines the size of avalanches may be some kind of inhomogeneity.When the pile is small, the size of avalanches is small because the uneven distribution of particles on the surface may be the dominant inhomogeneity of the system. When the pile becomes large, however, the deep inside of the pile is tightened and consolidated while the part near the surface is never tightened because of the repeated avalanches. The contrast in strength becomes the main factor of the inhomogeneity.