Tailings dams are potential facilities capable of failure, with the potential to generate high-impact environmental, economic, and social catastrophes given that they do collapse. In this study, numerical simulations of tailings as non-Newtonian fluids based on the Herschel–Bulkley model have been carried out to characterize the runout distances under different physical conditions. Using scaling arguments, a mathematical expression formed by three dimensionless groups including dimensionless yield stress, a modified Reynolds number , and the angle of the inclination of the system is proposed to explain the runout distance in tailings dams. The subsequent results show a good correlation between the variables, allowing us to deduce a high influence of the yield stress and the slope, albeit reflected both in the modified Reynolds number and the yield coefficient. Finally, a simple mathematical model is obtained from multidimensional analysis and the possibility of an abacus for regular intervals is proposed, which in turn supports an additional complement to the existing models for estimating the runout distances. • Prediction of dam breaking in mining. • Runout distances using CFD. • Dense suspensions in mining.