Minimum-Time Path (Brachistochrone) Analysis for Extreme Flow Slide Mobility in High-End Waste Dumps: Integrating Pore Pressure and Dynamic Rheology

Abstract High mobility in flow slides from high-end waste dumps often arises from complex interactions among pore pressure, basal friction, and path geometry. This study introduces a minimum-time path (Brachistochrone) reference, adapted from classical frictionless descent theory, to quantify how real flow slides deviate from an idealized baseline. Analysis of 46 documented events incorporates Bishop’s pore pressure coefficient and a velocity-dependent (Voellmy) rheology, revealing threshold conditions for extreme mobility. The results show that pore pressure ratios exceeding 0.4 and basal friction angles below 10° correlate strongly with increased mobility, particularly where narrow path apertures intensify velocity and turbulence. By contrasting observed runout distances with the Brachistochrone-based frictionless reference, these findings highlight the significance of liquefaction-prone conditions and provide field-oriented guidelines for dynamic friction angle selection, turbulence calibration, and pore pressure estimation. This approach offers a clearer theoretical basis for predicting flow slide mobility in active mining environments, supporting more effective risk management and design practices. Highlights Refines the classification system for flow slide mobility using a database of 46 coal mine waste dump failures in the Canadian Rockies. Explores the interplay of path geometry, pore pressure, and basal shear resistance in influencing flow slide mobility, offering practical guidelines and fitting equations. Highlights the significant role of turbulence and path aperture in the dynamic behavior of flow slides.