Analyzing the Diversion Effect of Debris Flow in Cross Channels Utilizing Two-Phase Flow Theory and the Principle of Energy Conservation

The movement process of debris flow in the complex roads system is important for risk evaluation and emergency rescue. This paper presents an in-depth study of the diversion effect of debris flow in cross channels, a common branching structure in both natural and engineered environments, especially in the field of urban debris flow prevention. A mathematical model is established based on the conservation of mass, momentum, and energy, and a solid–liquid two-phase motion equation for debris flow is derived from two-phase flow theory. A numerical solution method, combining the finite difference method and finite volume method, is employed to discretize and solve the equation. The model’s validity and effectiveness are confirmed through a numerical simulation of a typical engineering case and comparison with existing experimental data or theoretical results. This study reveals that debris flow at cross channels exhibits a diversion phenomenon, with some debris flow continuing downstream along the main channel and some diverting into the branch channel. The diversion rate, defined as the ratio of outlet flow to inlet flow of the branch channel, indicates the magnitude of this effect. This research shows that the solid–liquid ratio, inflow, width ratio, height ratio, and angle of the cross channel significantly impact the diversion effect. A series of numerical simulations are conducted by altering these parameters as well as the physical properties of debris flow and boundary conditions. These simulations analyze changes in flow rate, velocity, pressure, and other parameters of debris flow at cross channels, providing insights into the factors and mechanisms influencing the diversion effect. This research offers a robust instrument for comprehending and forecasting the dynamics of urban debris flows. It contributes significantly to mitigating the effects of debris flows on city infrastructure and enhancing the safety of city dwellers.