The non-homogeneous debris flows, consisting of a wide range of grain size, bulk density and demonstrating non-uniform velocity distributions, are commonly modeled as the two-phase flow. In adopting such an approach, a critical grain diameter to separate the solid and liquid phase, within such debris flows, can be determined through the principles of minimum energy dissipation. In the current study, an improved analytical approach using the resistance formula of water flow and mass conservation law is presented to determine the velocity of the solid and liquid phases within a non-homogeneous debris flow, based on the derived critical grain diameter. Some of the dynamic parameters required in the analysis are validated against the experimental data of a non-homogeneous, two-phase debris flow measured from the Jiangjia gully, Yunnan Province of China. The results show that, for the majority of non-homogeneous debris flows tested, the liquid phase exhibits higher velocity than the solid phase. However, as the bulk density of the debris flow increases, the solid phase tends to have higher velocity than the liquid phase. These findings are shown to have important implications on the vertical grading patterns of the bed deposits in depositional areas. The observations from the field studies indicate that the non-homogeneous debris flows with bulk density being significantly lower, close to and significantly higher than the critical value seem to exhibit normal (i.e. bed-to-surface vertical fining), mixed, and inverse (bed-to-surface vertical coarsening) grading patterns in the alluvial fan deposits.
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