An energy-based approach to predict debris flow mobility and analyze empirical relationships

Several empirical relationships allowing a preliminary estimate of debris flow runout distances have been proposed to correlate the runout length to the volume of the sliding granular mass, delimit potentially hazardous areas, and design safeguarding measures. To overcome their large variability and define their fields of applicability, an energy-based model, predicting debris flow mobility, is developed. The power balance of a granular mass sliding along two planar surfaces is written by taking into account the volume of the debris mass, the slopes of the sliding surfaces, an assigned interstitial pressure, the possible mass variation along the motion, the energy dissipation due to the grain inelastic collisions (“granular temperature” within a basal “shear layer”), and friction. A system of ordinary differential equations is obtained; its numerical solution allows, through parametrical analyses: (i) highlighting of the role of physical and mechanical parameters on the runout distance, such as grain size material, interstitial pressures, grain collisions, and erodibility of the crossed channel; and (ii) defining of the favourable conditions for debris flows mechanism generation. Finally, through the back-analysis of some cases, an original relationship to estimate the runout length, as well as to interpret the results of the empirical formulas, is proposed.