Optimization of an empirical equation in drop shape theory and a structural–mechanical analysis of a caved ore and rock particle flow system

The void ratio of the caved ore and rock particle system, which is a common and critical factor affecting draw, has not received much attention. In this paper, numerical draw tests were conducted to investigate the flow mechanism of caved ore and rock under varying void ratios. The study established a quantitative relationship between the void ratio of the particle system and the shape evolution of the isolated extraction zone (IEZ). To optimize the empirical equation for the IEZ shape, the drop shape (DS) theory was employed. Furthermore, a structural-mechanical analysis of the packing and flow particle systems was performed using the statistical mechanics method. The results demonstrated the following findings: (1) The void ratio significantly impacts the structural-mechanical characteristics of the gravity flow systems. As the void ratio increases, the IEZ shape transitions from a DS to an approximately ellipsoid shape and eventually to an upside-down DS. (2) With an increasing void ratio, the packing system of the caved ore and rock tends to become isotropic. This leads to a decrease in the degree of order, average coordination number, and average stress. (3) Notable correlations and consistency are observed in the laws governing the evolution of stress.