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| Titel |
A Two-Phase Solid/Fluid Model for Dense Granular Flows Including Dilatancy Effects |
| VerfasserIn |
Anne Mangeney, Francois Bouchut, Enrique Fernandez-Nieto, Gladys Narbona-Reina |
| Konferenz |
EGU General Assembly 2015
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 17 (2015) |
| Datensatznummer |
250114309
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| Publikation (Nr.) |
 EGU/EGU2015-14629.pdf |
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| Zusammenfassung |
| We propose a thin layer depth-averaged two-phase model to describe solid-fluid mixtures such as debris flows. It
describes the velocity of the two phases, the compression/dilatation of the granular media and its interaction with
the pore fluid pressure, that itself modifies the friction within the granular phase (Iverson et al., 2010).
The model is derived from a 3D two-phase model proposed by Jackson (2000) based on the 4 equations of mass
and momentum conservation within the two phases. This system has 5 unknowns: the solid and fluid velocities,
the solid and fluid pressures and the solid volume fraction. As a result, an additional equation inside the mixture is
necessary to close the system. Surprisingly, this issue is inadequately accounted for in the models that have been
developed on the basis of Jackson’s work (Bouchut et al., 2014). In particular, Pitman and Le replaced this closure
simply by imposing an extra boundary condition at the surface of the flow. When making a shallow expansion,
this condition can be considered as a closure condition. However, the corresponding model cannot account for a
dissipative energy balance.
We propose here an approach to correctly deal with the thermodynamics of Jackson’s equations. We close
the mixture equations by a weak compressibility relation involving a critical density, or equivalently a critical
pressure. Moreover, we relax one boundary condition, making it possible for the fluid to escape the granular media
when compression of the granular mass occurs. Furthermore, we introduce second order terms in the equations
making it possible to describe the evolution of the pore fluid pressure in response to the compression/dilatation of
the granular mass without prescribing an extra ad-hoc equation for the pore pressure. We prove that the energy
balance associated with this Jackson closure is dissipative, as well as its thin layer associated model. We present
several numerical tests for the 1D case that are compared to the results of the model proposed by Pitman and Le.
Bouchut, Fernandez-Nieto, Mangeney, Narbona-Reina, 2014, ESAIM: Mathematical Modelling and Numerical Analysis, in press.
Iverson et al., 2010, J. Geophys. Res. 115: F03005.
Jackson, 2000, Cambridge Monographs on Mechanics.
Pitman and Le, Phil.Trans. R. Soc. A 363, 1573-1601, 2005. |
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