Microtomography-based Discrete Element Modeling to Simulate Snow Microstructure Deformation Alsidqi Hasan1, Bruno Chareyre2, Janek Kozicki2, Fr´ed´eric Flin1, F´elix Darve2, Jacques Meyssonnier3 1
Centre d’Etudes de la Neige, CNRM-GAME URA 1357, M´et´eo-France - CNRS, 38400 Saint Martin d’H`eres, France, 2Laboratoire 3S-R UMR 5521, CNRS - UJF - INPG, 38041 Grenoble cedex 9, France, 3LGGE UMR 5183, UJF - CNRS, 38402 Saint Martin d’H`eres, France
[email protected] Summary Snow is a complex material composed of ice particles that exhibit intricate mechanical responses due to its internal and external forces. Mechanical solicitations and thermodynamics cause the ice particles to deform. A novel Discrete Element Method (DEM) based on experimental set-up parameters is developed to simulate creep and metamorphism in snow assembly. It employs a micromechanical model (as the model of Johnson and Hopkins, 2005) but uses real shape elements to mimic the ice particles of the experimental sample. The real shape elements are obtained by scanning the sample in three-dimensional (3D) high resolution images utilizing Synchrotron X-ray Microtomography technique.The simulations show good results to capture a complex microstructure deformation behavior of snow. Snow Metamorphism
Snow Creep I Snow
Creep: Slow deformation of ice particles under constant load (e.g, self weight) with time. It affects problems such as avalanche, densification, hydrology, etc. I Problems: How to simulate the phenomena using a better approach. I Objectives: To explain how snow deforms at particle scale in the ductile regime due to creep and to interpret the behavior through micro-scale DEM numerical simulations.
0.025
Contact geometry: Forces are computed based on relative displacement between particles (Cundall and Strack, 1979) Contact model: Elastic mechanism is applied for normal and bending and viscoelastic mechanism is applied for shear and twist. Simulation algorithms are made in C++ and incorporated in an open source framework of YADE (https://yade-dem.org; see also Kozicki and Donze, 2008) OA (UA ,
A
)
I Snow
Metamorphism: Continuous transformation of ice particles with time, which strongly impacts the physical and mechanical properties of snow. Thermodynamics is the main cause of the metamorphism but mechanical solicitations also modify the geometry of the ice matrix, thus influence its thermodynamics. I Problems: How to take into account the internal mechanical effects in modeling the metamorphism of snow. I Objectives: To explain the metamorphism by taking into account the micro-scale mechanical model using DEM.
E = 1e9 Pa, η = 0.7e16 Pa s E = 1e9 Pa, η = 2.2e16 Pa s E = 1e9 Pa, η = 3.7e16 Pa s
0.020
T
n
n
s
P
C
conta ct pla ne
OBC
OB (UB ,
Flow chart of DEM for creep
Creep Simulation Parameters Parameter Symbol Value Elastic modulus Viscosity Density (ice) Time step
E η ρ dt
Unit
0.25, 0.5, 1 x109 0.64, 2.2, 3.7 x1016 920 5x10−9 0.025
10
B
Pa Pa s kg m−3 s
E = 0.25e9 Pa, η = 2.2e16 Pa s E = 0.5e9 Pa, η = 2.2e16 Pa s E = 1e9 Pa, η = 2.2e16 Pa s
0.020
6 Load (N)
Particles are segmented experimentally via Diffraction Contrast Tomography (DCT) technique: it is capable of visualizing/detecting crystallographic orientation of each snow particle (Ludwig et al., 2009, Rolland et al., (in press))
Deformation
8
0.015
0.010
4
0.005 2
0.000 0
0 0
Converting particle image into DEM el.
Future Works For Snow Creep: I Validate DEM elements evolution with particles from the experiments (particle scale validations). I Model snow particles as flexible body (being carried out). For Snow Metamorphism: I Couple the DEM with the curvature-driven snow metamorphism algorithms. I Apply sample with bigger images and/or more particles to the DEM simulation. I Solve the problem related to boundary conditions (field conditions). I Apply the DEM simulations to different temperatures, type of snow (e.g., fresh snow is very sensitive to mechanical arrangements), snow density, etc.
10000 20000 30000 40000 50000 60000 70000
10000 20000 30000 40000 50000 60000 70000 Time (s)
Simulation loading cycle
Time (s)
Simulation with different elastic moduli
Acknowledgments This study is supported under the framework of the “Snow-White” project (ANR-06-BLAN0396) of the French “Agence Nationale de la Recherche” (ANR). The authors are particularly grateful to the scientists (J. Baruchel, E. Boller, W. Ludwig, S. Rolland du Roscoat, X. Thibault) of the ESRF ID19 beamline, where the 3D images have been obtained. Special thanks are also due to C. Brutel-Vuilmet, A. Dufour, B. Lesaffre and A. Philip who played a significant role in the experiments.
)
0.015
0.010
Simulation without mechanical model (gravity only) (Flin, 2004; see also Vetter, 2010)
0.005
0.000 0
10000 20000 30000 40000 50000 60000 70000 Time (s)
Simulation with different viscosities
Maxwell-Kelvin-Voigt packing model E = 1e9 Pa, η = 4e14 Pa s Experiment
1.8e-05
Converting a 3D snow particle to a DEM element: DEM element is obtain from voxels at the exterior surface of the 3D image
0.07
η, η1 η, η2
L1
U
L2
U
L2
U
L2
0.06
1.6e-05
0.05
1.4e-05 Deformation
dA
Deformation
M t, M b
Viscosity (η1, η1) of the packing model
OAC
1.2e-05
1.0e-05
Flow chart of DEM for metamorphism
0.03
0.02
8.0e-06
6.0e-06 5.0e+15
0.04
0.01
0.00
1.5e+16
2.5e+16
3.5e+16
Viscosity (η) of the contact model (Pa s)
Packing vs. Contact model viscosities
0
10000
20000
30000 Time (s)
40000
50000
60000
Validation
Conclusion: I The novel DEM technique based on experimental set-up parameters has shown good results to simulate a dynamic model of creep mechanisms of snow particles packing. I The DEM simulation was able to capture the complex creep behavior of snow particles packing using a simple contact model. I The deformation-time behavior of the simulations indicates a favorable agreement with the combined Maxwell and Kelvin-Voigt material packing model. I One can predict the viscosity of packing model from the contact model (correlated).
Evolution of the ice matrix during isothermal metamorphism (Flin et al., 2004; see also Kaempfer and Schneebeli, 2007; Chen and Baker, 2010; Vetter, 2010)
Breaking and consolidating of neck between two spheres during metamorphism (using curvature-driven snow metamorphism, Flin et al., 2003) DEM simulation of free fall of snow particles (gravity and micromechanical model) Modeling the metamorphism of fresh snow (Flin et al., 2003)
Remarks: The work is being carried out at the Centre d’Etudes de La Neige (CEN, M´et´eo France)
References Cundall, P.A., and Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique, 29(1), 47-65 (1979) Chen, S., and Baker, I.: Evolution of individual snowflakes during metamorphism. J. Geophys. Res., 115, doi:10.1029/2010JD014132 (2010) Flin, F., Brzoska, J.-B., Lesaffre, B., Col´eou, C., and Pieritz, R.A.: Full three-dimensional modelling of curvature-dependent snow metamorphism: first results and comparison with experimental tomographic data. J. Phys. D: Appl. Phys., 36, A49-A54 (2003) Flin, F., Brzoska, J.-B., Lesaffre, B., Col´eou, C., and Pieritz, R.A.: Three-dimensional geometric measurements of snow microstructural evolution under isothermal conditions. Ann. Glaciol., 38, 39-44 (2004) Flin, F.: Description physique des m´etamorphoses de la neige `a partir d’images de microstructures 3D naturelles obtenues par microtomographie X. Th`ese, (2004) link: http://www.cnrm.meteo.fr/cen/microstructure/these/flin these pdf.zip Johnson, J.B., and Hopkins, M.A.: Identifying microstructural deformation mechanisms in snow using discrete-element modeling. J. Glaciol. 51(174), 432-442 (2005) Kaempfer, T.U., and Schneebeli, M.: Observation of isothermal metamorphism of new snow and interpretation as a sintering process. J. Geophys. Res., 112, (2007) Kozicki, J., and Donze, F.V.: A new open-source software developed for numerical simulations using discrete element modeling methods. Comput. Methods Appl. Mech. Eng. 197, 4429-4443 (2008) Ludwig, W.,Reischig, P., King, A., Herbig, M., Lauridsen, E.M., Johnson, G., Marrow, T.J., and J. Y. Buffi`ere: Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis. Rev. Sci. Instr. 80, 033905 (2009) Rolland du Roscoat, S., King, A., Philip, A., Reischig, P., Ludwig, W., Flin, F., and Meyssonnier, J.: Analysis of Snow Microstructure by Means of X-Ray Diffraction Contrast Tomography. Adv. Eng. Mater. (in press) Vetter, R., Sigg, S., Singer, H.M., Kadau, D., Hermann, H.J., and Schneebeli, M.: Simulationg isothermal aging of snow. EPL. 89, (2010)
