Analysis of the statistics of sandpile avalanches using soil-mechanics results and concepts.
Analysis of the statistics of sandpile avalanches using soil-mechanics results and concepts.
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使用土壤力学结果和概念分析沙堆雪崩的统计数据。
DOI：
10.1103/physreva.43.2720
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
P. Evesque
中科院分区：
文献类型：
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作者：
P. Evesque
玻璃球雪崩的实验研究使用了一个鼓部分填充珠和旋转缓慢（Ω）围绕其水平轴。雪崩特性的统计（即，持续时间D和尺寸δΘ）已经被确定为旋转速度Ω、球体直径d和滚筒长度l的函数。这些统计量的宽度很宽，但雪崩不表现出周期性或1/f噪声。我们还得出结论，雪崩是由惯性和重力控制的。我们回顾土力学的经典结果;我们将看到，三轴试验结果，连同所谓的“临界状态”的粒状材料和Granta砾石模型的沙堆将明显和量化的摩擦，笼，和粘性颗粒样品中的众所周知的效果。使用这些既定的结果，特别是那些“临界”状态的土壤，我们将证明，桩的最大休止角可能会超过摩擦角的初始密度足够的材料，但这会导致灾难性的事件（雪崩）。这种临界状态的方法也使我们能够与平均雪崩的平均角度，平均雪崩持续时间，使用惯性过程，并预测雪崩持续时间。根据我们的模型，雪崩的大小是由真实的堆比容v和“临界”状态v c之间的差异控制的;宏观雪崩是在v< v c（即一阶过程）的情况下得到的，但我们预计当v= v c（即二阶跃迁）时会出现临界涨落（可能还有1/f噪声）。这一理论使得沙堆雪崩的自组织临界性理论和实验数据之间的联系，它也链接到库仑方法的自由表面的稳定性和雷诺发现的粘性效应。
Glass-sphere avalanches have been studied experimentally using a drum partly filled with beads and rotating slowly (Ω) around its horizontal axis. The statistics of the avalanche characteristics (ie, duration D and size δΘ) have been determined as a function of the rotation speed Ω, the sphere diameter d, and the drum length l. The widths of these statistics are broad, but avalanches do not exhibit either periodicity or 1/f noise. We conclude also that avalanches are governed by inertia and gravity. We recall then classical results of soil mechanics; we will see that triaxial test results, together with the so-called ‘‘critical state’’of granular material and the Granta gravel model of sandpiles will make evident and quantify the well-known effects of friction, caging, and dilatancy in granular samples. Using these established results, especially those on the ‘‘critical’’state of soil, we will demonstrate that the maximum angle of repose of a pile may exceed the angle of friction for initially dense enough materials, but that this leads to a catastrophic event (avalanche). This critical-state approach also allows us to relate the mean angle per avalanche to the mean avalanche duration, using an inertial process, and to predict the avalanche duration. According to our model, the avalanche size is controlled by the difference between the real pile specific volume v and that of the ‘‘critical’’state v c; macroscopic avalanches are obtained for v< v c (ie, a first-order process), but we expect critical fluctuations (and probably 1/f noise) when v= v c (ie, a second-order transition). This theory makes a link between the theory of self-organized criticality of sandpile avalanches and experimental data; it links also the Coulomb approach of the stability of a free surface and the dilatancy effect discovered by Reynolds.