Debris-flow modeling is a great challenge due to its complex physical mechanism that remains poorly understood. The present research incorporates the effect of rheological features of the non-Newtonian fluid into the complete quasi-single-phase mixture model, which explicitly accommodates the interactions between flow, non-uniform sediment transport, and bed evolution. The effect of rheological features is estimated by Hersch–Bulkley–Papanastasiou model that can be simplified to Bingham or

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... nian models with specific coefficients. The governing equations are solved by a fully conservative numerical algorithm, using an explicit finite volume discretization with well-balanced slope-limited centered scheme combined with an implicit discretization method. One set of large-scaled U.S. Geological Survey debris-flow experiments is applied to investigate the influence of the non-Newtonian fluid on debris-flow modeling. It is found that the present model closed by Hersch–Bulkley–Papanastasiou model performs better than the models without considering effect of rheological features, which may facilitate the development of quasi-single-phase mixture modeling for debris flows.