Department of Physics, Emory University, Atlanta, GA 30322, USA.
Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.
Soft Matter. 2017 Jul 26;13(29):5008-5020. doi: 10.1039/c7sm01060e.
We revisit the problem of the stress distribution in a frictional sandpile with both normal and tangential (frictional) inter-granular forces, under gravity, equipped with a new numerical method of generating such assemblies. Numerical simulations allow a determination of the spatial dependence of all the components of the stress field, principle stress axis, angle of repose, as a function of systems size, the coefficient of static friction and the frictional interaction with the bottom surface. We compare these results with the predictions of a theory based on continuum equilibrium mechanics. Basic to the theory of sandpiles are assumptions about the form of scaling solutions and constitutive relations for cohesive-less hard grains for which no typical scale is available. We find that these constitutive relations must be modified; moreover for smaller friction coefficients and smaller piles these scaling assumptions break down in the bulk of the sandpile due to the presence of length scales that must be carefully identified. Fortunately, for larger friction coefficient and for larger piles the breaking of scaling is weak in the bulk, allowing an approximate analytic theory which agrees well with the observations. After identifying the crucial scale, triggering the breaking of scaling, we provide a predictive theory to when scaling solutions are expected to break down. At the bottom of the pile the scaling assumption breaks always, due to the different interactions with the bottom surface. The consequences for measurable quantities like the pressure distribution and shear stress at the bottom of the pile are discussed. For example one can have a transition from no dip in the base-pressure to a dip at the center of the pile as friction increases.
我们重新研究了在重力作用下具有法向和切向（摩擦）相互作用的摩擦沙堆中的应力分布问题，配备了一种生成这种组件的新数值方法。数值模拟允许确定应力场的所有分量、主应力轴、休止角的空间依赖性，作为系统尺寸、静态摩擦系数和与底部表面的摩擦相互作用的函数。我们将这些结果与基于连续平衡力学的理论预测进行了比较。沙堆理论的基本假设是关于无粘性硬颗粒的缩放解的形式和本构关系的假设，对于这些颗粒，没有典型的尺度。我们发现这些本构关系必须修改；此外，对于较小的摩擦系数和较小的沙堆，由于必须仔细识别的长度尺度的存在，这些缩放假设在沙堆的大部分中会失效。幸运的是，对于较大的摩擦系数和较大的沙堆，在大部分中，缩放的破坏是微弱的，允许一个近似的分析理论与观察结果很好地吻合。在确定了触发缩放破坏的关键尺度之后，我们提供了一个预测理论，以确定何时可以预期缩放解失效。在沙堆的底部，由于与底部表面的不同相互作用，缩放假设总是会失效。我们讨论了对可测量量（例如沙堆底部的压力分布和剪切应力）的影响。例如，随着摩擦的增加，从底部压力没有凹陷到沙堆中心有凹陷可以发生转变。
