to the late 1960s was largely in response to needs

did measure Young's modulus of snow in static

arising from the expansion of U. S. military activi-

uniaxial compression tests. Later, Yosida et al.

ties in the polar regions. The sheer size of the

(1956) discussed the interpretation of the four-

Soviet Union, and its range of arctic, subarctic

parameter model and found the parameters for it

and alpine environments, made the study of snow

from creep tests on snow under uniaxial com-

mechanics important in that nation, although, un-

pressive stress. Bader (1962a) also suggested that

fortunately, only a small fraction of the resulting

the one-dimensional hyperbolic sine relationship:

literature is available in translation.

= ε o sinh (Aσ)

The objective of most of the work through this

(1)

period was to determine the parameters required

(where ε is the strain, σ is the stress and *t *is time

and εo and *A *are constants) might be used to

viscoelasticity to problems involving snow me-

chanics. The effort followed the recognition that

describe creep in snow; that is, it could replace

some patterns of deformational behavior in snow

the linear relationship for the dashpot of the Max-

samples in a laboratory or field setting could be

well element of the four-parameter model. Mellor

described by linear relationships. For example,

(1964) introduced an additional term into eq 1 by

Bader et al. (1939) discussed the creep of snow

dividing the coefficient of the hyperbolic sine by

a viscosity coefficient, η. He also discussed the

(they used the term "plasticity") in connection

with investigations of snow settlement. They did

use of exponential and power relationships to

experiments on samples in both uniaxial confined

represent compactive viscosity (i.e., the viscosity

and unconfined compression, but since they did

determined from the compaction of natural snow-

not attempt to formulate a constitutive relation-

packs, or from confined compression experiments

ship to describe the process there was no frame-

in the laboratory) in terms of the snow density as

work within which parameters could be defined.

derived from data sets collected by various inves-

Thus, they made no mention of any particular

tigators. Other determinations of the constants

mechanical property or constitutive relationship,

for the four-parameter model from creep test data

although the patterns of deformation certainly

have been done in Russia by Kuvaeva et al. (1967)

suggested a combination of linear elastic and vis-

and by Shinojima (1967). Parameters for these lin-

ear relationships, along with the available values,

cous behavior. In fact, Yosida et al. (1956) were

are summarized in Appendix B.

able to use data from Bader et al. (1939) to calcu-

Even as efforts continued to find parameters

late values for the coefficient of Newtonian vis-

for linear relationships, it was apparent that the

cosity of snow.

ranges were too limited to solve many problems

The most general constitutive relationship used

in snow mechanics. Bader (1962a) recognized the

for snow prior to about 1970 was the equation for

problem and suggested that the ranges of the lin-

a four-parameter viscoelastic fluid with linear ele-

ear relationships might be extended if they were

ments (App. A). According to Yosida et al. (1956),

applied incrementally, as the values of the pa-

it was first used in snow mechanics by de

rameters change with deformation. We have found

Quervain (1946) to interpret the results of torsion

no references in which attempts to use this ap-

experiments.* Bucher (1948) included a sketch of

proach were made, although Desrues et al. (1980)

a Maxwell model (a spring and dashpot in series

did devise a similar method involving simple non-

as shown in Fig. A1 in App. A) and used the

linear relationships. Mellor (1975) stated that there

constitutive relationship for a linear viscous fluid

were still no alternatives to linear relationships,

to find the coefficient of Newtonian viscosity for

and that 1) there were no constitutive relation-

compacted snow as a function of temperature,

ships for use in solving problems involving mul-

duration of loading and a variety of types of snow,

tiaxial stress states, and 2) the data to develop

grain sizes, and ages. Interestingly, although the

such relationships did not exist. He credited B.

Maxwell model includes a spring element, Bucher

Salm with initiating efforts to address the need

made no mention of the elastic properties (or lack

for such relationships. In fact, Salm (1967) did

of them) of snow, although Yosida et al. (1948)

consider the extension of the hyperbolic sine rela-

tionship to cases of the creep of snow in triaxial

*Kuvaeva et al. (1967) reported that the viscosity of snow was

stress states. Later Salm (1971) used the relation-

first determined by "the group of K. S. Zavriev in 1937."

ships in exponential form to develop a failure

Unfortunately, the reference they gave for this work appears

criterion based on energy storage and dissipa-

to be incorrect and we could not locate the paper.

3