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

Abstract

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.Key words: sliding granular mass, granular temperature, shear layer, collisions, empirical relationships.Résumé : Plusieurs relations empiriques permettant d'effectuer une estimation préalable des distances parcourues par les écoulements de débris ont été proposées pour mettre en corrélation la distance parcourue par les écoulements et le volume de masse granulaire glissante, délimiter les zones potentiellement dangereuses et mettre en place des mesures de protection. Pour compenser la grande variabilité de ces relations et définir leurs champs d'application, on conçoit un modèle basé sur l'énergie, capable de prédire la mobilité des écoulements de débris. On décrit l'équilibre des forces d'une masse granulaire glissant sur deux surfaces planes en tenant compte du volume de la masse de débris, de l'inclinaison des surfaces de glissement, d'une valeur déterminée de pression interstitielle, de la possible variation de masse sur le parcours de l'écoulement, de la dissipation d'énergie due aux collisions inélastiques entre grains (« température granulaire » au sein d'une « couche de cisaillement » basale) et des frottements. On obtient un système d'équations différentielles ordinaires; la solution de ce dernier permet, par le biais d'analyses paramétriques : (i) de souligner le rôle des paramètres physiques et mécaniques (tels que la taille des grains de la masse glissante, les pressions interstitielles, les collisions entre grains, l'érodabilité du canal croisé) sur la distance du parcours des écoulements; (ii) de déterminer les conditions favorables au déclenchement du mécanisme d'écoulement de débris. Enfin, grâce à l'analyse rétrospective de certain...

Estimation of the velocity at the impact of high rate sliding granular masses

“…' being the effective normal stress; M b , the dynamic friction angle at the base of the granular mass. In collisional regime, the stress component normal to the boundary ("dispersive pressure") and the shear stress component are expressed as follows [14]: [15,16]; rheological models where both the frictional and collisional contributions are coupled into a single term, are also available [17]. Rapid change of pores volumes related to the continuous grains rearrangement [18] within the shear layer can generate excess pore water pressures at the base of coarse-grained material flows.…”

“…Conversely, the consolidation process of fine-grained materials [22][23], along the motion, progressively reduces the pore water pressure; the corresponding increase of the shear strength causes a reduction of the travelled distance. For materials, characterized by d p < 0.02 m, the energy dissipation due to grain collisions can be neglected [16].…”

“…Both proposed models are based on the following hypotheses ( Fig. 2a): (i) the sliding granular mass is represented by a block (parallelepipedal shape) of thickness h, length l and width b (d w is the depth, from the upper surface of the block, of the groundwater); (ii) the granular flow runs along planar surface of constant slope D and length L (deformations induced by the possible variations of sliding surface are neglected [24]); (iii) although it is well-known that the mass of a debris flow may change due to erosion or deposition processes [12,16], for the sake of simplicity, the debris flow mass is assumed constant.…”

Grain-Size Analysis of Debris Flow Alluvial Fans in Panxi Area along Jinsha River, China

“…A larger ε indicates a debris flow with greater transport energy. This equation considers the grain size data including its distribution shape and the mean grain size, which corresponds to references [19][20][21]. Table 6 shows that ε ranges from approximately 3.6 to 53, with the highest value in Type III and the lowest value in Type V. The grain index values for Types I and III are almost at the same level, which is greater than those of Types II, IV, and V. ε is only related to the characteristics of the accumulation fan (i.e., the parameters from the grain-size distribution analysis).…”

Laboratory investigation of performance of a screen type debris-flow countermeasure

“…( [2][3][4][5][6]); empirical or analytical approaches to quantify the mobility of debris-flow, e.g. ( [7][8][9][10][11][12]); mapping of debris-flow hazard zones, e.g. ( [13][14][15][16][17][18]; investigation of debris-flow triggering causes, e.g.…”