Abstract:

Granular matter is widely present in nature and human production and life. It exhibits many mechanical properties that differ from those of conventional solids and liquids. Janssen effect is one of the important and well-known phenomena that demonstrates the unique static mechanical properties of granular matter. Researchers have conducted in-depth studies on this effect from various perspectives, including theoretical models and computer simulations. “Chopstick rice-lifting” is an interesting physical phenomenon closely related to the Janssen effect. However, existing research lacks a quantitative analysis of this phenomenon, particularly regarding the discussion of the critical depth. In this paper, the actual system involved in “chopstick rice-lifting” is simplified into a system composed of a silo, grains, and a lifting rod, and the Janssen continuum model is employed to conduct a static mechanical analysis of this system, leading to the theoretical derivation of a transcendental equation concerning the critical depth. Subsequently, by combining experimental data with the numerical solution of this transcendental equation, the authors explore how the Janssen coefficient and critical depth of the granular system in the experiment vary with relevant physical quantities. The results indicate that the Janssen coefficient under different experimental conditions fluctuates slightly around an average value 1.16; and that, when the diameter of the lifting rod is held constant, an increase in the diameter and mass of the silo results in a higher total mass of both the grains and the silo, thereby increasing the critical depth. Conversely, when the diameter of the silo is constant, an increase in the diameter of the lifting rod leads to a decrease in the total mass and an increase in the contact area between the lifting rod and the grains, resulting in a decrease in the critical depth. The theoretical calculation results are generally consistent with the experimental measurement results.

Key words: granular material, Janssen’s continuum model, Janssen effect, critical depth