Natural lateral particle segregation commonly occurs during the hydraulic deposition of slurry and thickened tailings in surface tailings storage facilities (TSFs), producing spatial heterogeneity in physical, hydrogeotechnical, and mineralogical properties, as well as in the water table. In sulfide-rich tailings, such heterogeneity complicates the design of reclamation cover systems, which are themselves affected by it. This study investigates the impact of physical and rheological properties of hard-rock mine tailings slurries on their segregation under hydrodynamic conditions. It proposes a multiparametric equation for the segregation index (SI) based on Buckingham's π-theorem. For this purpose, six flume experiments were conducted using tailings with initial solids mass concentrations of 63%, 66%, and 69% at slopes of 0.5% and 1%. Results revealed strong exponential correlations (R² > 0.95) between SI and tailings' physical properties (solids concentration, bulk density) as well as rheological parameters (Herschel–Bulkley yield stress and flow index, Cross infinite dynamic viscosity). The SI equation was developed using MATLAB nonlinear least-squares optimization with a trust-region reflective algorithm. Using an SI threshold of 0.05 to define non-segregating behavior, the proposed model can predict segregation tendencies as a function of tailings properties and slope conditions. Further laboratory and field investigations are needed to validate and generalize the criterion.