An integrated hydrodynamic model for runoff-generated debris flows with novel formulation of bed erosion and deposition

Debris flow is one of the most common geohazards in mountainous regions, posing significant threats to people, property and infrastructure. Among different types of debris flows, runoff-generated debris flows are attributed to rain storms, which provide abundant runoff that entrain large quantities of bed material, resulting in the formation of a solid-liquid current known as a debris flow. One of the keys to effectively simulating runoff-generated debris flows is modelling the erosion-deposition process. The commonly used approach for formulating erosion and deposition, although constrained by physics, suffers from a singularity in the presence of vanishing velocity, which poses a major challenge for practical applications. It is also argued that the deposition rate cannot be represented by simply reversing the sign of the erosion rate. To address these two issues, we have developed a depth-averaged debris flow model with a novel method of calculating the erosion-deposition rate. We have demonstrated that the singularity is due to the non-linear erosion-deposition term but quickly disappears while the flow converges to the equilibrium that is defined by the classic Takahashi's formula. To resolve the non-linearity and avoid the singularity, an implicit method within a Godunov-type finite volume framework has been proposed. An additional parameter is introduced to differentiate the erosion rate from the deposition rate. The model is validated against several test cases, including a real-world debris flow event. Satisfactory results are obtained, demonstrating the model's simulation capability and potential for wider applications such as risk assessment and impact-based early warning.