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Volume 18, issue 1 | Copyright
Nat. Hazards Earth Syst. Sci., 18, 303-319, 2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 22 Jan 2018

Research article | 22 Jan 2018

Comparing thixotropic and Herschel–Bulkley parameterizations for continuum models of avalanches and subaqueous debris flows

Chan-Hoo Jeon1,2 and Ben R. Hodges2 Chan-Hoo Jeon and Ben R. Hodges
  • 1Division of Marine Science, The University of Southern Mississippi, 1020 Balch Blvd, Stennis Space Center, Mississippi 39529, USA
  • 2Center for Water and the Environment, The University of Texas at Austin, Austin, Texas 78712, USA

Abstract. Avalanches and subaqueous debris flows are two cases of a wide range of natural hazards that have been previously modeled with non-Newtonian fluid mechanics approximating the interplay of forces associated with gravity flows of granular and solid–liquid mixtures. The complex behaviors of such flows at unsteady flow initiation (i.e., destruction of structural jamming) and flow stalling (restructuralization) imply that the representative viscosity–stress relationships should include hysteresis: there is no reason to expect the timescale of microstructure destruction is the same as the timescale of restructuralization. The non-Newtonian Herschel–Bulkley relationship that has been previously used in such models implies complete reversibility of the stress–strain relationship and thus cannot correctly represent unsteady phases. In contrast, a thixotropic non-Newtonian model allows representation of initial structural jamming and aging effects that provide hysteresis in the stress–strain relationship. In this study, a thixotropic model and a Herschel–Bulkley model are compared to each other and to prior laboratory experiments that are representative of an avalanche and a subaqueous debris flow. A numerical solver using a multi-material level-set method is applied to track multiple interfaces simultaneously in the simulations. The numerical results are validated with analytical solutions and available experimental data using parameters selected based on the experimental setup and without post hoc calibration. The thixotropic (time-dependent) fluid model shows reasonable agreement with all the experimental data. For most of the experimental conditions, the Herschel–Bulkley (time-independent) model results were similar to the thixotropic model, a critical exception being conditions with a high yield stress where the Herschel–Bulkley model did not initiate flow. These results indicate that the thixotropic relationship is promising for modeling unsteady phases of debris flows and avalanches, but there is a need for better understanding of the correct material parameters and parameters for the initial structural jamming and characteristic time of aging, which requires more detailed experimental data than presently available.

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Short summary
This work shows that a multiphase flow solver using a multi-material level-set method with yield-stress models of non-Newtonian viscosity provides a means for numerical approximation of avalanches and subaqueous debris flows. This simulation approach was tested with both time-independent and time-dependent models of viscosity. Moreover, two different approaches were used to evaluate the Coussot parameters. Overall, the numerical results showed reasonable agreement with prior experimental data.
This work shows that a multiphase flow solver using a multi-material level-set method with...