A Discrete Element Method For Snow Mechanics

1. A Discrete Element Method For Snow Mechanics Jerome B. Johnson Mark A. Hopkins U. S. Army ERDC-CRREL

2. Important Motivating Questions Why study snow mechanics? What is the discrete element method (DEM)? Why use DEM instead of continuum mechanics? Will the DEM replace continuum descriptions?

3. Snow Mechanics Applications Vehicle mobility. Evolution of thermal and radiation properties. Snow loads on structures. Construction of snow roads, runways, tunnels, foundations. Shock wave propagation and attenuation. Avalanche release and flow.

4. Tire/Snow Interaction

5. The Discrete Element Method A representation of the dynamics of an assemblage of discrete particles Complex particle shapes Particle contact physics

6. Why DEM Instead of Continuum? Material inhomogeneity Coupled shear and bulk deformation effects Evolution of material state through failure and deformation Complex particle contact physical processes

7. Sources of Material Inhomogeneity

8. Identifying Material Inhomogeneity

9. Structural Inhomogeneity Strength Scaling

10. Structural and Material Property Inhomogeneity

11. Coupled Shear and Bulk Deformation

12. Evolution of Material State:Snow Shear The shear stress with a normal stress demonstrates many of the complexities associated with snow deformation. The effects of displacement rate, temperature, normal stress, and initial density can be seen in the figure. In the left figure the vertical displacement decreases as the shear stress increases (i.e., the sample density is increasing). Eventually the shear stress plateaus. The shear stress with a normal stress demonstrates many of the complexities associated with snow deformation. The effects of displacement rate, temperature, normal stress, and initial density can be seen in the figure. In the left figure the vertical displacement decreases as the shear stress increases (i.e., the sample density is increasing). Eventually the shear stress plateaus.

13. Complex Physical Processes

14. Particle Contact Physics Sintering (empirical-Gubler, 1982) Temperature range 0 to -40 deg. C Shear (grain boundary sliding: elastic-Newtonian viscosity) Tensile (elastic-brittle rupture) Bending (elastic-brittle rupture) Torque (elastic-Newtonian viscosity) Compression (elastic-power law creep)

15. Particle Contact Sintering

16. Particle Contact Bond Growth

17. Compression-Power Law Creep

18. Particle Contact Shear

19. Discrete Element Snow Modeling Three-dimensional, discrete elements Ice particles are axisymmetric cylinders with variable aspect ratio. Particle orientation specified using quaternions (4 parameter representation of floe orientation) Dynamics of system evolves from contact and body forces on particles (F=ma at each contact)

20. Discrete Element Snow Modeling Particles interact through frozen and un-frozen contacts. Contacts initially unfrozen. Freezing occurs on contact (later dependence on temperature, pressure, and duration of contact). Model can simulate failure of snow samples. (Later evolution of particle shapes due to metamorphosis

21. Frozen Contacts Linear viscous-elastic force connecting particles. Force proportional to the diameter of the frozen contact. Contact supports moment. Contact diameter variable (later with time, temp., and pressure). Location of contact fixed to particle surfaces, however, location is subject to non-linear viscous contact creep in tangential direction. Particle contacts break when maximum stress exceeds tensile strength.

22. Un-Frozen Contacts Linear viscous-elastic force normal to particle surfaces. Coulomb friction tangential force.

23. Ice particles are axisymmetric cylinders whose shape can change

24. Begin simulation with particles distributed uniformly in space. Space contracts to reach desired density.

25. Sample at 35% solid fraction. Sample is periodic in all three directions.

26. Pressure on Sample. Relaxation begins at 150 s.

27. Slice through model compared to slice through snow sample.

28. Simulation of shear box tests by placing top and bottom surfaces on the sample. The surfaces are loaded in the normal direction and then sheared at a constant rate.

29. The DEM/Continuum Relationship Continuum Less computer intensive Good representation of homogeneous material DEM Accurate physics with explicit implementation Accurate representation of microscale mechanisms Accurate development of effective continuum constitutive relationships

30. Conclusions DEM can be used to improve the physical basis for snow mechanics calculations At present, particle contact physics and bulk structure is qualitative DEM implements contact physics in a qualitative way Contact physics algorithms need further experimental development