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

This article focuses on investigating the influence of void ratio on the flow mechanism and structural-mechanical characteristics of caved ore and rock particle systems in underground caving mining. Through isolated numerical draw tests using a rolling resistance model, the study establishes a quantitative relationship between the void ratio and the shape evolution of the isolated extraction zone (IEZ), extending the upside-down drop shape (UDDS) theory to drop shape (DS) theory. Findings indicate that as the void ratio increases, the IEZ shape transitions from a DS to an approximately ellipsoid shape and then to a UDDS, accompanied by increased maximum width, height, and longitudinal asymmetry. Structural analyses reveal that higher void ratios lead to more isotropic packing systems with decreased order, coordination number, and average stress, while stress arching effects correlate with changes in the IEZ and isolated movement zone (IMZ) shapes. The results provide theoretical and technical insights for optimizing underground mine design, predicting ore loss and dilution, and advancing the understanding of granular flow in mining and related fields.