Numerical Analysis of Debris-Flow Erosion in Nonuniform Erodible Beds with Concave and Convex Slopes: A Comparison of Four Dynamic Models

Debris flow can entrain large amounts of loose material from the channel bed or lateral banks due to their extreme sediment transport capacity and thus amplify its magnitude and destructive potential. Most dynamic models assume an infinite bed with a uniform slope, neglecting the influence of nonuniform bed morphology with concave or convex slopes that exist in natural debris flow channels. In this study, the applicability of four dynamic models, namely, the Cao model, Hsu model, Medina model, and Li model, in nonuniform channels are compared based on flume experimental and field measurements from a numerical approach. The erosion depths obtained from the Cao model and Hsu model significantly differ from the experimental measurements. In contrast, the modeling results of the Medina and Li model closely match the experimentally measured variables. In the case of a natural debris flow event, the simulation results of the Medina model and Li model are compared. Differences in the distributed entrained volumes are primarily observed in the lower part of the channel, possibly due to more pronounced momentum growth after massive entrainment and velocity increases in steep upstream sections. Four local concave or convex profiles along the debris-flow routing channel demonstrate that the maximum entrainment rate does not occur at sites with the steepest bed slope but at the slope angle transition points, indicating that the Li model is more suitable for quantitatively describing debris-flow entrainment in a nonuniform channel with longitudinal inflexions. Our research may provide valuable insights into debris-flow entrainment modeling and stimulate further efforts in the intricate quantification of the entrainment process.