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Two-Layer Flow Model

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A debris front passes a concrete check dam at the Illgraben test site on August 20, 2020. Note the blocky front and watery tail. The frontappears to dam the muddy fluid flowing behind; the rocks in the tail appearing completely submerged in the muddy fluid. Saturation increases from front to tail.

We propose a dilatant, two-layer debris flow model validated by full-scale density/saturation measurements obtained from the Swiss Illgraben test site. Like many existing models, we suppose the debris flow consists of a matrix of solid particles (rocks and boulders) that is surrounded by muddy fluid. However, we split the muddy fluid into two fractions. One part, the inter-granular fluid, is bonded to the solid matrix and fills the void space between the solid particles. The combination of solid material and inter-granular fluid forms the first layer of the debris flow. The second part of the muddy fluid is not bonded to the solid matrix and can move independently from the first layer. This free fluid forms the second layer of the debris flow. During flow the rocky particulate material is sheared which induces dilatant motions that change the location of the center-of-mass of the solid. The degree of solid shearing, as well as the amount of muddy fluid and of solid particles, leads to different flow compositions including debris flow fronts consisting of predominantly solid material, or watery debris flow tails. De-watering and the formation of muddy fluid washes can occur when the solid material deposits in the runout zone. After validating the model on two theoretical case studies, we show that the proposed model is able to capture the streamwise evolution of debris flow density in time and space for real debris flow events.

 
The debris flow is divided into a serie of volumes V. The flowing material is separate into two layers. The first layer is composed by all the solid mass (particles and boulders) and inter-granular fluid (hsb), while the second layer is only composed by free fluid, (hf), flowing on top of the first one. The density of the first layer can vary from dense flowing configurations (front of the debris flow) to wet flowing configurations (tail of the debris flow) under dilatancy.
 
Sketch of two different debris flow configurations, possessing the same amount of solid and fluid mass. The left one is a dilated configuration, happening during flowing, while the right one is the reference configuration, called the co-volume configuration, typically when the flow is at rest. The red dots show the center of mass of the corresponding configuration. The parameters z is the difference between the centers of mass of the dilated and co-volume configuration.