Dynamic interaction and synergistic screening mechanism of segregation and penetration of thick granular materials

• A composite vibration parameter captured periodic screening responses. • Six parameter regimes separated low-, transitional-, and high-rate screening. • Fine-particle passing progressed from burst to concentrated to dispersed stages. • A stable near-screen particle-size structure reflected balanced stratification and penetration. • A dynamic segregation index linked stronger separation to lower screening. Vibrating screens are widely used for particle-size classification, yet the nonlinear coupling between vibration amplitude and frequency, together with the dynamic evolution of particle-size composition within the bed, limits the applicability of conventional vibration parameters and segregation indices. In this study, the segregation and undersized-particle penetration dynamics of a binary mixed-particle bed under different vibration conditions were investigated using the discrete element method. An empirical composite vibration parameter (ECVP) A d 1 × f d 1.87875 was developed based on the multipeak-multitrough evolution of screening-rate curves to unify the characterization of screening-state transitions under different frequency–amplitude combinations. The screening process was further divided into three stages: early burst penetration, intermediate concentrated penetration, and late dispersed penetration. A dynamically stable particle-size structure was identified in the near-screen region during the concentrated-penetration stage, suggesting an approximate dynamic balance between fine-particle penetration in the lower bed and fine-particle settling or segregation in the overlying region. Accordingly, a novel dynamic segregation index (DSI) Δ ĥ incorporating mean particle height and volume fraction was proposed. The results demonstrate that the combined use of the ECVP, DSI, and fine-particle height statistics enables the screening process to be classified into low-rate, transitional, and high-rate regimes. These findings provide theoretical support for optimizing vibrating-screen operating parameters and elucidating the synergistic mechanisms of particle segregation and undersized-particle penetration.