Avalanche simulationM. Rentschler, Ch. Ancey, S. Cochard

Environemental hydraulics laboratory, EPFL, Switzerlandmartin.rentschler@epfl.ch

LABORATOIREYDRAULIQUE

NVIRONNEMENTALEEH

Abstract

To tackle the delicate issue of avalanche simulation we are investigating the dynamics of this kind of phenomena on the lab scale, which enables us to make reproducible experiments under well-controledlaboratory conditions. More specifically we focus our attention on the motion of an avalanching mass flowing down an inclined plane (channelized or not), with a significant slope change in its lower part. Velocity(front and free surface) and the flow depth can be accurately measured at any point using image processing techniques. In the meantime, we extend numerical tools (three-dimensional Navier-Stokes solver) tomodel this experiment. The final objective is to understand the dynamics of complex fluids far from equilibrium (no steady regime is achieved) and develop governing equations that are more appropriate to thatpurpose than the classical shallow-water equations.

1. Natural Phenomena

Figure 1: Avalanche in the test field of the SLF in the Vallee dela Sionne(Valais). (Courtesy of SLF)

Very expensive Experiments (Costs of about 60000 SFr)

Not reproducible

Uncertainties on the initial conditions

Large number of involved processed

Few parameters that can be conveniently measured

2. Isolated process: Viscoplastic flow

( a ) Carbopol deposit ( b ) Avalanche deposit

Viscoplastic flow

Avalanche deposits on an inclined terrain (plastic behavior)Avalanche flows like a viscoplastic fluid

Carbopol

Yield-stress τ0

No ThixotropyReproducible and stableEasy to handle: No melting, not poisonous...

Rheological properties of the Carbopol

τ0

ViscosityµShear Stressτ

0

20

40

60

80

100

120

140

160

180

200

10−5 10−4 10−3 0.01 0.1 1 10 1001

10

100

1000

104

105

106

She

arS

tres

sτ[P

a]

Shear-rateγ [1/s]

Vis

cosi

tyµ

[Pa/

s]

Figure 3: Rheometrical measurements for a Carbopol sample.The lines represent the fitted Herschel-Bulkley model.

Herschel-Bulkley model

If |τ | < τ0: γ = 0,

If |τ | > τo: τ = τ0 + K|γ|1n

3. Experimental device

Inclined plane

Figure 4: The inclined plane with Steve Cochard.

Variable inclination

Various geometries

Very short time to open the gate

Measuring the free surface

Camera

Projector

Inclined plan

Fluid

Reservoir

Dam(open)

Figure 5: Measuring the free-surface evolution using imageprocessing techniques.

Pattern projection

Recording the deformation of the pattern

Calculating the position of the free surface

( a ) ( b ) ( c )

Figure 6: (a) Projection on the plane, (b) same projection onthe surge, (c) resulting free surface height.

4. Numerical Simulation

Numerical treatment

Algorithm:

Semi implicit incompressible Navier-Stokes solver

Finite Volume on rectangular staggered grid

Level-Set representation of the free surface

Turbulence model via turbulent viscosity

Parallel computing

Model:

Shear rate dependent viscosity function:For the Herschel-Bulkley model:

µ =τ0 + |γ|

1n

|γ|

Surface tension

Numerical results

0.01 1.0Viscosity [Pa s]

Figure 7: Dam break of viscoplastic material. Snapshot showingthe collapse and spreading of a viscoplastic fluid along a horizon-tal plane.

5. Conclusion

We developed a framework that is a first stab at modeling rapidgravity-driven mass movements (such as snow avalanches) onthe laboratory scale. The objective is to gain insight into thedynamics of complex (nonlinear) fluids in non-steady flows andto propose governing equations that overcome the current lim-itations of flow-dynamics models, which are usually based onthe shallow-flow approximation and near-equilibrium regime as-sumption. For that purpose, we work in two complementary di-rections:

We built an experimental facility (inclined planes), which canbe operated to create fluid avalanches in the laboratory (finitevolume of material instantaneously released). Specific imageprocessing techniques have been developed to measure thefree-surface evolution and track the front position and velocity.On the short term, additional parameters such as the velocityprofile inside the flowing material could be probed, still usingimage processing techniques.

We extend a Navier-Stokes solver primarily developed at theUniversity of Bonn (NaSt3D) to cope with nonlinear rheologies.The front and free-surface boundaries conditions pose seriousproblems from the numerical point of view. On the short term,we should be able to use this code for simulating avalancheson the lab scale. On the long term, we are thinking abouta mix numerical code, which combines both two-dimensional(flow-depth averaged) and three-dimensional capacities withina single tool.

References

[1] C. Ancey. Powder-snow avalanches: approximation as non-Boussinesq clouds with a Richardson-number-dependententrainment function. Journal of Geophysical Research,109(F01005), 2004.

[2] C. Ancey, S. Cochard, S. Wiederseiner, and M. Rentschler.Existence and features of similarity solutions for non-Boussinesq gravity currents. submitted to Physica D, 2006.

[3] C. Ancey, S. Cochard, S. Wiederseiner, and M. Rentschler.Front dynamics of supercritical non-Boussinesq gravity cur-rents. Water Resources Research, 42, W08424, 2006.,42(W08424), 2006.

[4] C. Ancey and M. Meunier. Estimating bulk rheological prop-erties of flowing snow avalanches from field data. Journal ofGeophysical Research, 109(F01004), 2004.

[5] S. Cochard and C. Ancey. Accurate measurements of free-surface in the dam-break problem. In A.H. Cardoso, ed-itor, River Flow 2006 - International Conference on Flu-vial Hydraulics, volume 2, pages 1863–1872, Lisbon, 2006.Balkema.

[6] R. Croce, M. Griebel, and M. A. Schweitzer. A Parallel Level-Set Approach for Two-Phase Flow Problems with SurfaceTension in Three Space Dimensions. Preprint 157, Sonder-forschungsbereich 611, Universitat Bonn, 2004. submitted.

SGR 2006, Annual Meeting of the Swiss Group of Rheology, 20th October, 2006, University Fribourg, Switzerland In Cooperation with: