A series of two-phase models for grain-fluid flows with dilatancy
Résumé
Debris flows are a growing natural hazard due to climate change and population den-
sity. To effectively assess this hazard, simulating field-scale debris flows at a reasonable
computational cost is crucial. We enhance existing debris flows models by rigorously de-
riving a series of depth-averaged shallow models with varying complexities describing the
behavior of grain-fluid flows, considering granular mass dilatancy and pore fluid pressure
feedback. The most complete model includes a mixture layer with an upper fluid layer and
solves for solid and fluid velocity in the mixture and for the upper fluid velocity. Simpler
models are obtained by assuming velocity equality in the mixture or single-layer descrip-
tions with a virtual thickness. Simulations in a uniform configuration mimicking submarine
landslides and debris flows reveal that these models are extremely sensitive to the rheology,
the permeability (grain diameter), and initial volume fraction, parameters that are hard to
measure in the field. Notably, velocity equality assumptions in the mixture hold true only
for low permeability (corresponding to grain diameters d = 10−3 m). One-layer models
results can strongly differ from those of the complete model, for example the mass can stop
much earlier. One-layer models however provide a rough estimate of two-layer models when
permeability is low, initial volume fraction is distant from critical, and upper fluid layer is
very thin. Our work demonstrates the need of developing two-layer models accounting for
dilatancy and accounting for an upper layer made either of fluid or grains.
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