changes in bond structure limited. In such cases,
A descriptive model for
the constitutive equations for linear-elastic, vis-
snow deformation
Based on the studies cited above, the micro-
cous or viscoelastic materials can be used to inter-
structural deformation of a snow sample during a
pret the test results as described previously (see,
hypothetical experiment in uniaxial compression
for example, Yosida et al. 1956, Shinojima 1967,
can be described. Our purpose is to highlight the
Kuvaeva et al. 1967, Kry 1975b). However, if the
problems involved in characterizing the deform-
snow has been compacted, plowed, wind-blown,
ational properties of a material like snow that can
or otherwise processed and is well-bonded and of
occur in many forms. For simplicity, temperature
high density, then even relatively large stresses
and loading rate are assumed to be constant and
can be sustained without significant deformation
the grains in the sample are initially bonded into
or changes in bonding (Abele and Gow 1976). In
chain structures (Akitaya 1974, Kry 1975b).
these cases, linear relationships are probably ap-
There are several paths that the deformation
plicable over a relatively large range of stresses.
can follow as the load increases. The bonds be-
Unfortunately, in most applications involving
tween grains can deform so that they thicken or
natural snow, the strain is large enough that sig-
thin according to their orientation with respect to
nificant changes in the bonding and deformational
the loading. Alternatively, fracture of the bonds
properties occur throughout the deformational
will permit grains to be displaced with respect to
process and linear relationships apply only over a
each other and grains can break, changing the
limited range of deformation. Thus, either gen-
grain size distribution (Kinosita 1967). Bond ge-
eral nonlinear constitutive relationships that span
ometry can also change by sintering at a rate that
the entire range of behavior are needed or, as
depends on the temperature and the pressure at
suggested by Bader (1962a) simple linear rela-
grain contacts. In fact, for a test in which the
tionships may be used incrementally as deforma-
deformation mechanisms operate at low rates, it
tion increases.
is possible that the changes in bonding from sin-
tering can be more important than those due to
the deformation.
SOME CASE HISTORIES
The overall effect of the deformation is to
ILLUSTRATING THE USE
tighten the structure and increase the density of
OF SNOW MECHANICS
the snow. Concurrently, the bonding changes so
that the mechanical properties of the snow can
Despite the impediments that exist and make
vary through a wide range of values, depending
snow mechanics difficult to use, it has been ap-
on the deformation path. For example, Salm (1977)
plied to a diverse range of problems (vehicle mo-
found a 20% change in the viscosity of a snow
bility, foundations, tunnels, creep loading of struc-
sample due to 1% deformation in uniaxial com-
tures, roads and runways, snow removal, impact
pression.
and explosive shock loading, avalanche release,
As the deformation process continues, an ap-
construction of snow structures, and interpreta-
parent relationship between density and mechani-
tion of seismic and acoustic signals). Here we
cal properties may be established. The reason this
give an overview of three engineering topics that
relationship seems to exist is that both the me-
illustrate the success, and the recurring problems,
chanical properties and the density depend on
in trying to apply snow mechanics.
the nature of the bonding/grain contacts. Thus, it
is the bonding, and not the density, that is the
Snow creep forces on
critical variable, suggesting that some parameter
avalanche structures
that represents the influence of the bonding should
One of the problems which prompted the start
replace the density in plots of snow strength or
of formal study of snow mechanics was the deter-
other properties.
mination of snow creep forces acting on fixed
The macroscopic deformation of a snow sample
structures designed to prevent snow avalanches
reflects the accumulated deformation on the scale
(Bader et al. 1939). Initial attempts to calculate
of the grain size. The relationship between the
snow forces on avalanche structures were made
macroscopic deformation and the stress is used to
by assuming that a snow block, between two infi-
determine the parameters for constitutive rela-
nitely long containing walls, with dry sliding re-
tionships. In general, if tests on natural snow are
sistance at the base, acted on the downslope re-
of short duration, then strains are small and
sisting structure. The model predicted a linear
6
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