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\begin{document}

\title{A Unified Mean Velocity Equation of Debris Flows on the Basis of
Physical Mechanics: Inspirations from some Arguments and Data collection}



\author[1]{Chao Ma}%
\author[2]{Lv Miao}%
\author[3]{Cui Du}%
\author[4]{Liqun Lyu}%
\affil[1]{School of soil and water conservation, Beijing Forestry University}%
\affil[2]{School of Soil and Water Conservation, Beijing Forestry University}%
\affil[3]{School of Civil Engineering, Henan University of Science and Technology}%
\affil[4]{Beijing Forestry University}%


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  \date{May 27, 2024}


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\begin{abstract}
The physical mechanics and velocity of debris flow are crucial for
debris flow mitigation measures. The two aspects closely relate to the
grain composition, density, and flow depth. We present a combined
research on Manning coefficient, debris flow classification, and mean
velocity using mechanical analysis. Comparison of Manning coefficient
reveals that it varies greatly at the same observation site and given
event. The reciprocal Manning coefficients for viscous flows in Jiangjia
Ravine, China, are the highest among the observation sites at a given
flow depth. The stony debris flows in Kamikamihorizawa, Japan, are
mainly governed by inertial stress, whereas the viscous debris flows in
Jiangjia Ravine and Wudu, China, are mainly governed by friction stress.
The reciprocal Manning coefficient of stony debris flows in
Kamikamihorizawa, but not of viscous debris flows in China, increases
with increasing Savage and Bagnold numbers. The reciprocal Manning
coefficient decreases with the Friction number for both viscous and
stony debris flows. Based on dimensionless parameters, we proposed
debris flow classification from the perspective of physical mechanics
including friction- and inertial stress-dominated flows. Finally, a new
debris flow mean velocity equation was developed considering the
characterizing diameter parameters (D\textsubscript{10},
D\textsubscript{50}), density, flow depth, and channel gradient. This
equation performs well and could be updated in the future if the
observed data of friction- and inertial stress-dominated flows are
available. The results of this work can help strengthen the resistance
of debris flows in different flow regimes.%
\end{abstract}%



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