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Discrete Modeling Research
Snow
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More than 40% of the
northern hemisphere is affected by seasonal snow, including
the U.S., Canada, most of Europe, and northern Asia (Turkey,
Iran, Afghanistan, and Russia). The presence of snow strongly
affects vehicle mobility, sensors, and the ground state
in winter and in mountains. Our goal is to develop an accurate
snow model that can be used to solve problems that depend
on the ability to realistically simulate snow deformation,
metamorphosis, and electromagnetic and radiative interaction.
We have developed a three-dimensional discrete-element-based
(DEM) snow model that differs from all other snow models
in having an explicit geometric structure composed of a
large aggregate of discrete, individual snow grains. The
model contains the fundamental grain-scale processes that
underlie snow deformation. Interactions between grains
are governed by contact algorithms for sintering, deformation,
and failure. Consequently, this model can be used to investigate
problems in which knowledge of the microstructure of the
snow is important, such as dynamic simulations of the interaction
of tires and tracks with snow and calculations of snow
grain surface-to-volume ratios important in electromagnetic
and radiative processes. These processes are impossible to
simulate using continuum models. We have used the model to
perform simulations of snow settlement, shear, and micro-penetration
that qualitatively reproduce experimental results.
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Below are links to two Power Point Presentations
on Discrete Element (DEM) snow modeling:
Click on Picture above for Power Point presentation:
A Discrete
Element Method for
Snow Mechanics I
Click on Picture above for Power Point presentation:
A Discrete
Element Method for
Snow Mechanics II
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The
DEM technique is a logical tool to use to simulate snow because,
in addition to employing the grain-scale process models, it has an explicit
geometric structure that is composed of individual ice grains
and grain clusters and that evolves with deformation and metamorphosis.
The DEM model snow consists of a large assembly of grains with
an arbitrary mixture of axisymmetric particle shapes, including
spheres, tapered cylinders, and elongated or oblate spheroids
and ellipsoids. Grains translate and rotate in space in response
to contact and body forces. Over the past several years we have
determined the important microscale processes that affect snow
sintering and the micromechanical properties of snow from the
literature on laboratory and field tests. We have developed dynamic
constitutive models that simulate grain boundary sliding, power
law creep, grain rotation, and viscous-elastic bond deformation and
failure in tension, compression, bending, and twisting, and grain-to-grain
sintering.
The contact force model has the following structure. Pairs of grains
interact through unfrozen and frozen viscous-elastic contacts.
Forces are calculated with respect to a plane of contact tangent
to the surface of each grain. At unfrozen contacts there are compressive
forces normal to the plane of contact and frictional sliding forces
in the plane of contact. At frozen contacts there are tensile
and compressive forces in the direction normal to the plane of
contact, tensile forces in the plane of contact, a twisting moment
about the normal to the plane of contact, and a bending moment
about an axis in the plane of contact. Each component of the force
and moment at a frozen contact has an associated failure mechanism
based on tensile strength and an associated viscous creep mechanism
that acts to relax stress. The frozen contact is circular. The
growth of the circular contact area is governed by the sintering
model and depends on time, temperature, and contact pressure.
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Model
Snow Samples
Currently,
model snow samples are created by populating a cubic lattice
with randomly sized and oriented particles, giving them
small random velocities, and contracting them to the desired density.
(Click on Figure 1 to see the building of a model snow sample.)
Frozen bonds are generated on contact. Initial bond areas
are uniformly distributed. Values for the micromechanical
parameters were taken from macroscale test data for snow
and ice, as microscale test data is not yet available. We
use empirical sintering data because the controlling physical
mechanisms for sintering in snow are not well defined. Figure
2 shows a stereographic slice through the model snow sample.
We have used the model to perform simulations of a micro-penetrometer
in snow (Figure 3) and a snow-filled shear box (Figures
4 and 5) that qualitatively reproduce experimental results.
This is a severe test of the snow model since either dilation
or contraction and either strain hardening or softening
can occur, depending on strain rate and temperature. We are able
to replicate these behaviors in simulations, which cannot be done
using previous methods. Currently, the snow model does not
use a metamorphosed microstructure or grain shape for lack
of information. In addition, the parameters for the micromechanical
processes and sintering are not accurately known since the
necessary experiments have not been performed. However,
we have started an experiment to determine grain scale parameters
by measuring the micromechanical properties of snow. Our-long
term goal is to develop a virtual snow that can simulate
metamorphosis, fluid and vapor flow, heat conduction, and
electromagnetic properties.
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Figure 1. Model snow sample creation. Click
on the image above to watch snow sample creation by
populating a lattice with random Particles (14.3 MBytes).
Click here
to see a rotation of the completed model snow sample (8.6
MBytes).
Figure
2. A stereographic slice through a model
snow sample. (The porosity is 70%.) Click on the
figure above to see the
slice move through the model snow sample (4.6 MBytes).
Figure 3.
A large model snow sample with a
1 cm diameter micro-penetrometer.
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Figure 4. A model snow sample after settlement.
The box is 20 mm wide. The grains are 1 mm in diameter.
During settlement, porosity decreased from 70% to 61%,
while the coordination number increased from 3.21 to
4.71. Click on the figure above
to view a movie of the settling process (3.2 MBytes).
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Figure 5. The sample in Figure 4 after 20%
shear. The coordination number further increased to
4.98. Click on the figure above to
view a movie of the shear process (3.3 MBytes).
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Principal Investigators:
Dr. Jerome Johnson
has worked at the Cold Regions Research and Engineering Laboratory
(CRREL) since 1983 and is a member of the Snow and Ice Branch.
His research focuses on solving applied problems relating to ice,
frozen ground, snow, and other granular materials. Dr. Johnson
is a scientific editor for the Journal of Glaciology, a science team
member for the Mars CryoScout project, a former participating scientist
on the Mars Polar Lander Mission, and a consultant on the upcoming
Mars Rover mission.
Dr. Mark Hopkins
works in the Snow and Ice Branch at CRREL. His research is focused
on the development of discrete element modeling techniques and
the application of those techniques to simulate problems in sea
ice, river ice, and snow mechanics.
Collaborators:
Dr.
Dave Cole (CRREL) designs and conducts the small-scale
laboratory experiments for the snow modeling project and is an
expert on the mechanical and physical properties of ice and mechanical
testing methods. He has extensive experience conducting multi-scale
mechanical and structural tests on ice. He holds patents on test
apparatus design.
Dr. Randall
German is Brush Chair Professor in Materials and
Director for the Center for Innovative Sintered Products, Pennsylvania
State University. He has authored numerous articles and books on
the sintering of powders.
Dr.
Martin Schneebeli is a research scientist from the Swiss
Institute for Snow and Avalanche Research and is an expert in
characterizing snow microstructure and microstructural testing
techniques.
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References:
Hopkins, M.A. (in press)
Discrete Element Modeling With Dilated Particles, to appear
in the Journal of Engineering Computations.
Johnson, J.B.
and M.A. Hopkins (in prep.) A discrete element method model of
deformation for dry seasonal snow. Draft ERDC Technical Report.
Johnson, J.B.
and M. Schneebeli (1999) Characterizing the microstructural and
micromechanical properties of snow. Cold Regions Science and Technology,
30: 91-100.
Johnson, J.B.
(1998) A preliminary numerical investigation of the micromechanics
of snow compaction. Annals of Glaciology, 26: 51-54.
Shapiro,
L.H., J.B. Johnson, M. Sturm, G.L. Blaisdell (1997) Snow Mechanics:
Review of the state of knowledge and applications, United States Army
Corps of Engineers Cold Regions Research and Engineering Laboratory
(USACRREL), Report CR 97-03.
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Discrete
Element Research Page Snow and
Ice Branch
Contact Information
Dr. Mark A. Hopkins
Phone: 603-646-4249
Fax: 603-646-4644
E-mail: Mark.A.Hopkins@erdc.usace.army.mil
(Postal address below.)
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