The angle of repose—i.e., the angle θr between the sloping side of a heap of particles and the horizontal—provides one of the most important observables characterizing the packing and flowability of a granular material. However, this angle is determined by still poorly understood particle-scale processes, as the interactions between particles in the heap cause resistance to roll and slide under the action of gravity. A theoretical expression that predicts θr as a function of particle size and gravity would have impact in the engineering, environmental, and planetary sciences. Here we present such an expression, which we have derived from particle-based numerical simulations that account for both sliding and rolling resistance, as well as for nonbonded attractive particle–particle interactions (van der Waals). Our expression is simple and reproduces the angle of repose of experimental conical heaps as a function of particle size, as well as θr obtained from our simulations with gravity from 0.06 to 100 times that of Earth. Furthermore, we find that heaps undergo a transition from conical to irregular shape when the cohesive to gravitational force ratio exceeds a critical value, thus providing a proxy for particle-scale interactions from heap morphology.

休止角——即角度 θr一堆颗粒的倾斜面和水平面之间的距离——提供了表征颗粒材料的堆积和流动性的最重要的观察指标之一。然而，这个角度是由仍然知之甚少的粒子尺度过程决定的，因为堆中粒子之间的相互作用会导致在重力作用下滚动和滑动的阻力。预测的理论表达式θr作为颗粒大小和重力的函数，它会对工程、环境和行星科学产生影响。在这里，我们提出了这样一个表达式，该表达式是从基于粒子的数值模拟得出的，该模拟考虑了滑动和滚动阻力，以及非键合的有吸引力的粒子 - 粒子相互作用（范德华）。我们的表达式很简单，并再现了实验锥形堆的休止角作为粒度的函数，以及θr从我们的模拟中获得，重力是地球的 0.06 到 100 倍。此外，我们发现当内聚力与重力之比超过临界值时，堆会经历从锥形到不规则形状的转变，从而为堆形态的粒子尺度相互作用提供了一个代理。