4:15 PM - 4:30 PM
[MIS15-03] Development of a numerical model for mudflows based on a two-layer model
Keywords:Debris flow, Mudflow, Numerical model, Erosion and deposition
The fluidity of debris flows varies by grain size. In coarse-grained debris flows (boulderly debris flows), interparticle stresses predominate and particles flow in a layered manner. Numerical models of boulderly debris flows reflect this in the resistance law and incorporate the mechanism that erosion and deposition occur as the channel gradient approaches equilibrium bed gradient. The reproducibility of the models has been confirmed by application to debris flow events.
On the other hand, in fine-grained debris flows (mudflows), particles are suspended by turbulence. It has been pointed out that mudflows contain high concentrations of sediment and cannot be explained by the theory of low-concentration turbulent suspension flow. Therefore, there is a need to develop a numerical model that appropriately reflects the flow mechanism of mudflows. In this study, a numerical model incorporating the flow mechanism of mudflows as a high-concentration flow was developed based on flume experiments of mudflows.
First, a two-layer model of mudflow was developed based on experiments in which the pore pressure of debris flow was measured. The experiments covered a wide range of flows from boulderly debris flow to mudflows by varying the grain size. The results showed that the transition from boulderly debris flow to mudflow was continuous with a two-layered flow structure with turbulent flow in the upper layer and laminar flow in the lower layer, corresponding to the Reynolds number of the debris flow defined as the ratio of inertial stress and interparticle stress of the debris flow. Based on a two-layer model reflecting this two-layer flow, a flow model of mudflows was constructed in which the boundary position of the two layers is determined by the Reynolds number of the debris flow. When the two-layer model of mudflows was applied to a flume experiment of mudflow deposition, the equilibrium bed gradient calculated based on the two-layer model was able to explain the gradient of the mudflow deposition.
By incorporating the two-layer model of mudflows into the shallow-water equations, a numerical model of mudflows was constructed. Although the flow model is two-layered, the shallow water equation treats the mudflow as a single fluid and considers conservation of mass and momentum. The shallow-water equations employ a framework similar to that used for boulderly debris flow. Therefore, the effect of the two-layer model for mudflow is indirectly represented as the resistance law and the entrainment rate equations in the shallow-water equations.
On the other hand, in fine-grained debris flows (mudflows), particles are suspended by turbulence. It has been pointed out that mudflows contain high concentrations of sediment and cannot be explained by the theory of low-concentration turbulent suspension flow. Therefore, there is a need to develop a numerical model that appropriately reflects the flow mechanism of mudflows. In this study, a numerical model incorporating the flow mechanism of mudflows as a high-concentration flow was developed based on flume experiments of mudflows.
First, a two-layer model of mudflow was developed based on experiments in which the pore pressure of debris flow was measured. The experiments covered a wide range of flows from boulderly debris flow to mudflows by varying the grain size. The results showed that the transition from boulderly debris flow to mudflow was continuous with a two-layered flow structure with turbulent flow in the upper layer and laminar flow in the lower layer, corresponding to the Reynolds number of the debris flow defined as the ratio of inertial stress and interparticle stress of the debris flow. Based on a two-layer model reflecting this two-layer flow, a flow model of mudflows was constructed in which the boundary position of the two layers is determined by the Reynolds number of the debris flow. When the two-layer model of mudflows was applied to a flume experiment of mudflow deposition, the equilibrium bed gradient calculated based on the two-layer model was able to explain the gradient of the mudflow deposition.
By incorporating the two-layer model of mudflows into the shallow-water equations, a numerical model of mudflows was constructed. Although the flow model is two-layered, the shallow water equation treats the mudflow as a single fluid and considers conservation of mass and momentum. The shallow-water equations employ a framework similar to that used for boulderly debris flow. Therefore, the effect of the two-layer model for mudflow is indirectly represented as the resistance law and the entrainment rate equations in the shallow-water equations.