Voellmy-type mixture rheologies for dilatant, two-layer debris flow models

We formulate and test different Voellmy-type mixture rheologies that can be introduced into two-layer debris flow models. The formulations are based on experimental data from the Swiss Illgraben test site as well as on mathematical constraints in steady flow conditions. In agreement with the ideas of Iverson, we show that the uniform, fixed rheological models cannot accurately represent the changing frictional resistance when debris flows undergo spatial and temporal changes in solid-fluid composition. Indeed, the experimental results of Illgraben indicate that flow friction decreases with increasing volumetric fluid concentration; however, the degree of reduction depends on both the pore pressure and the solid particle agitation. The interplay between these processes makes friction in debris flows highly nonlinear and difficult to quantify. Changing the friction according to the flow composition must be carefully executed, because it can lead to numerical instabilities, which is a recurrent problem in two-layer debris flow models. We test the different rheological formulations using a real event documented with differential topographic data collected using unmanned aerial vehicles (UAVs). The model is able to reproduce the correct erosion pattern and exhibit the right density profile. The event includes de-watering at the front and deposition of sediment, which causes a change from debris flow to debris flood or hyperconcentrated flow, which indicates that two completely different flow states can be modeled with a single Voellmy-type mixture rheology.

Automated summary

We formulate and test different Voellmy-type mixture rheologies based on experimental data and mathematical constraints to accurately represent changing frictional resistance in debris flows. The experimental results indicate that flow friction decreases with increasing fluid concentration, but the reduction depends on both pore pressure and solid particle agitation. We carefully execute the changes in friction according to flow composition to avoid numerical instabilities, and use UAV-collected topographic data to test the different rheological formulations, successfully reproducing the correct erosion pattern and density profile.