compaction beneath the tire, a plane strain response
Porous elasticity accounts for the elastic properties
may be more appropriate for deep snow than for shal-
of materials that undergo large volume changes, such
low snow, as illustrated in the snow deformation
as fresh snow. To implement a porous elasticity
measurements in Figure 3. The DruckerPrager mate-
model, the additional parameters needed are the slope
rial cohesion d and the DruckerPrager material an-
of the elastic portion of the pressurevolume curve
gle of friction β can be calculated from
(during an unloadreload event, as illustrated in Fig-
ure 14); κ, representing the elastic portion of compac-
tan β = 1.73 sin φ
tion; and the elastic tensile limit, p el . The elastic
(19)
t
compaction value was not available since compaction
d = c 1.73 cos φ.
tests were performed under monotonic loading (no
(20)
unloading), so κ was chosen to provide realistic elas-
tic behavior within the stress ranges of the simula-
Acquiring apparent values for cohesion c' and fric-
tion angle φ' from shear loading of snow under a ve-
tions. The elastic tensile limit p el was chosen to be
t
the same as the same as tensile limit pt used to define
hicle tire and from a ring shear device is discussed by
the yield surface.
Blaisdell et al. (1990) and Alger and Osborne (1989).
Yield surface. The parameters defining the shear
Both methods were applied to field measurements on
portion of the yield surface for the DruckerPrager
undisturbed snow with a density ranging from 60 to
250 kg/m3 and temperatures from 2 to 16C. The
model can be calculated from the MohrCoulomb
cohesion c and the internal angle of friction φ, assum-
results are shown in Figure 22, along with the values
ing plane strain response and non-dilatant flow. Al-
used in the CRREL Shallow Snow Model (SSM 1.0)
though non-dilatant flow can be assumed for the
(Blaisdell et al. 1990).
Figure 22. Calculated c' and φ' using measurements
from the CRREL Instrumented Vehicle (CIV) and the
ring shear device and predicted using the Shallow
Snow Model, SSM 1.0. (From Blaisdell et al. 1990.)
14
Previous Page
