We performed a numerical study of the jamming that stops the flow of granular material from a three-dimensional hopper discharging due to gravity. When the hopper outlet is not much larger than the particles, granular material clogs the hopper outlet due to the formation of an arch or dome. For a wide range of particle diameters, we obtained the size distribution of the “avalanche,” defined as the number of particles that fall before jamming. We repeated this process through a discrete element method model verified with a simple experiment. From these distributions, we determined the probability of the flow jamming before N particles pass through the hopper. As the ratio between the hopper outlet diameter and the particle diameter increases, the probability that an arch will block the outlet decreases. We show here that the probability of one particle passing through the hopper is not constant when there are not sufficient particles. Then, we propose a new model that can quantify changes in particle passing probability. Using this model, we derive the particle passing probability in a hopper with shallow columns and confirm that the probability of one particle passing through the hopper is closely related to the pressure acting on the bottom of the hopper.

我们对卡纸进行了数值研究，该卡纸阻止了由于重力而从三维料斗中排出的颗粒状物料的流动。当漏斗出口不大于颗粒大时，由于形成拱形或圆顶，颗粒状物质会堵塞漏斗出口。对于较大的粒径范围，我们获得了“雪崩”的尺寸分布，“雪崩”的定义是在堵塞之前掉落的颗粒数量。我们通过经过简单实验验证的离散元方法模型重复了此过程。根据这些分布，我们确定了在N之前流阻塞的概率颗粒通过料斗。随着料斗出口直径和颗粒直径之间的比率增加，拱形堵塞出口的可能性降低。我们在这里表明，当没有足够的粒子时，一个粒子通过加料斗的概率不是恒定的。然后，我们提出了一个可以量化粒子通过概率变化的新模型。使用该模型，我们得出了浅料斗中颗粒通过的概率，并确认了一个颗粒通过料斗的概率与作用在料斗底部的压力密切相关。