This study explores the Brazil Nut Effect (BNE), a phenomenon where larger particles rise to the surface of a shaken mixture, by developing a theoretical framework and conducting experimental validation. Theoretical equations were derived to quantify the effects of vibration frequency, amplitude, particle size, and mass on the BNE. Experimental verification utilized a cement mortar vibration table and a binary particle system to analyze particle behavior under varying vibration conditions. Results demonstrated that the BNE is significantly influenced by the fourth power of particle diameter, particle mass, and vibration parameters. Observations aligned closely with theoretical predictions, confirming the validity of the framework. This research provides a generalized approach to understanding the BNE and establishes foundational insights for future computational simulations and broader applications in particle dynamics.