the axial viscosity is the viscosity of the dash-
YOUNG'S MODULUS AND
pot of the Maxwell model. The compactive vis-
POISSON'S RATIO
cosity is determined either from the results of
The plot of the data for both static and dy-
experiments in confined compression (uniaxial
namic measurements of Young's modulus for
strain), or from measurements of compaction as a
snow from Mellor (1975), supplemented by addi-
function of time for natural snowpacks.
tional data from Kuvaeva et al. (1967), is shown in
The data on axial viscosity are shown in Figure
Figure B1. In addition, the only data available
B3. The range of values for this parameter is large,
from dynamic or quasistatic determinations of
even allowing for the differences in the physical
Poisson's ratio for snow are also included in the
properties of polar and seasonal snow. It should
figure.
also be noted that, in addition to determining the
axial viscosity, Shinojima (1967) also did creep
experiments in torsion and uniaxial tension and
used the results to determine the parameters for
VISCOSITY
the four-parameter viscoelastic fluid model for all
The difficulty of determining Poisson's ratio in
three loading modes. In addition, the data were
rapid-loading compression tests, coupled with the
used to define the viscosity of the lead dashpot of
extreme compressibility of low density snow, led
the model as a function of temperature and snow
density over the range of temperatures from 0 to
to the introduction in Bader et al. (1951) of the
40C and densities from 125300 kg/m3. Note
parameter called the "cross section number (the
reciprocal of Poisson's ratio)." Mellor (1975) iden-
that these results were used by Lang and
tified this parameter as the viscous equivalent of
Sommerfeld (1977).
Poisson's ratio and presented the available data
Mellor (1975) determined the compactive vis-
(Fig. B2).
cosity of seasonal snow from data from field mea-
Mellor (1975) separated the data on viscosity
surements by Kojima (1967), and both field and
into the categories of "axial" and "compactive"
laboratory studies by Keeler (1969a). He combined
viscosity. The former refers to the viscosity de-
these results with data for polar snow from Bader
termined from the "steady state" creep rate in
(1962b), experimental work by Mellor and
experiments under constant uniaxial compressive
Hendrickson (1965) and other field studies, into
his Figure 11 (p. 266). Ambach and Eisner (1985)
stress. In terms of the four-parameter model,
Yosida (1963)
Calcullatted ffromData bbyDeQQuervain1(1966)
u a ed rom Data y de uervain ( 966)
*Shinojima (1967)
Incompressible
0.5
Uniaxial Tension*
0.4
0.3
?
Bader et al.
0.2
(1951)
2
Data Summarized by Roch (1948)
0.1
Uniaxial
Compression*
0
200
400
600
800
1000
Density (kg m 3 )
Figure B2. Mellor's (1975) summary of data on the viscous analog of Poisson's ratio.
Data sources were de Quervain (1966), Roch (1948), Shinojima (1967), Yosida (1963)
and Bader et al. (1951).
27
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