A predictive model for the sliding distance of tailings dam breaches incorporating progressive failure and energy conservation

The runout distance of tailings pond dam-break is a core parameter for defining the extent of disaster impact and also a frontier challenge in geohazard prevention and control research worldwide. Existing prediction methods mostly rely on empirical formulas or complex numerical simulations, lacking an analytical model that combines clear physical mechanisms with engineering practicality. This study decomposes landslide motion into two stages: acceleration and deceleration. Disintegration coefficients \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are introduced to quantify the energy dissipation during the progressive disintegration of the sliding mass in these two stages. Furthermore, by integrating the rigid-body energy balance relationship with the empirical disintegration coefficient \\(\\lambda_{1}\\) , which was calibrated through two sets of physical model tests and PFC2D numerical simulations, and by combining this with the residual internal friction angle \\(\\theta\\) corrected using test data, a progressive disintegration prediction model for landslide runout distance is established. The dam-break accident of the Zhen’an gold mine tailings pond in Shaanxi Province is taken as a case study for validation. The calculated results fall within a reasonable error range. Using this as the engineering baseline case, a global continuous perturbation sensitivity analysis is conducted with each parameter varied within ± 50%, revealing the nonlinear regulatory effects of key parameters on runout distance. The results indicate that, compared with other computational methods, the predictions of this model tend to be conservative, making it suitable for rapid preliminary assessment of dam-break hazards. This research provides theoretical support for risk zoning and emergency strategy formulation for tailings pond dam-breaks.