U.S. DEPARTMENT OF AGRICULTURE
FOREST SERVICE
ALTA AVALANCHE STUDY
Project B
Report No. 2
by
Edward R. LaChapelle and Ronald I. Perla
Wasatch National Forest
June 1967
Much progress has been made in forecasting
direct action soft slab avalanches from meteorological observations. Factors such as wind,
temperature and precipitation intensity are weighed against preset criteria and the hazard
is judged accordingly.
However, the interplay of meteorological factors is complex and standard meteorological
observations cannot be exclusively relied on for soft slab prediction. Ambient air
temperature for example, cannot be correlated with crystal structure which is determined
by upper atmospheric conditions. Also, because of radiation, air temperature may not be
indicative of the metamorphism of freshly deposited snow.
With present instrumentation the forecaster is hard-pressed to keep track of the various
crystal structure and property changes taking place during a storm. Besides basic changes
in dendritic structure, crystal layers will vary in such important modifying features as
degree of riming4, impurity concentration, wind fragmentation, wetness, and
clustering. Thus, a set of meteorological conditions measured at a convenient location
with convenient instruments could apply equally well to a variety of slabs which differ
from one another in many mechanical properties.
Measurement of the mechanical properties of newly deposited snow are needed to supplement
meteorological data and improve upon the predictability of soft slab release.
There is a scarcity of experimental data pertaining to properties of newly deposited snow
in the density range of 0.05 to 0.20 gm/cm3. Most of the information which
covers this low range is extrapolated from relationships derived from experiments on snow
with densities greater than 0.2 gm/cm3. Soft slab avalanches usually occur
during or immediately after a storm and involve snow in this low density range. Laboratory
experiments on fresh snow are difficult to set up, hence the development of "in
situ" experimental techniques are necessary.
Two problems are encountered in the setting up of consistent "in situ"
experiments. Figure 1. shows the first problem: Property and structure variation in the
z-direction. To solve the first problem requires gathering data at appropriate z
intervals. The second problem is property and structure variation in the x and y
directions. The solution of the second problem involves the choice of a suitable study
area, free of local wind anomalies; and the statistical design of the experiment to
account for X and Y data variations.
The drop cone penetrometer
The Haefeli ram penetrometer is a convenient device for measuring the strength of the snow
pack. In the Haefeli method, an impact energy is imparted to the ram and the corresponding
penetration is noted. From these data, strength as a function of z can be calculated for
the snow profile. These strength measurements are of great value to the avalanche
forecaster in evaluating climax and deep slab hazards. However, even if the Haefeli ram is
set gently on a fresh layer of snow, its narrow head may exert a pressure on an order of
magnitude greater than the resistive pressure of the snow.
At the Alta Avalanche Study Center an instrument, similar in operation to the Haefeli
penetrometer, was developed. This instrument, capable of measuring the strength profile of
a soft slab, is the drop cone penetrometer. Previous models of this instrument have had a
successful history of providing consistent fresh snow data.1,2,3
The sequence of operation for the Alta model (Figure 2) is as follows: The instrument
rests on the snow, supported by its flange in a level position. The cone assembly is held
up by the clamp. The operator looks through the observation window, loosens the clamp, and
gently lowers the cone assembly until it makes contact with the snow. The operator holds
the cone assembly in this position and notes the meter stick reading, designated Zr
to symbolize reference position. The cone assembly is then lifted to an initial Z1
reading on the meter stick, released and allowed to fall and penetrate the snow. The cone
assembly comes to rest at a meter stick position recorded as Z2. The cone
assembly is then lifted and clamped in the up position, the aluminum frame is picked up
and reset in a level position over a new sampling area, and the sequence is repeated.
if the weight of the cone assembly is w, the impact energy is given by:
U = w(Z2 - Z1)
and the penetration is:
Z = Z2 - Zr
Minimum input energy is obtained when
Z1 = Zr
U can be increased by decreasing Z1 (i.e. raising the cone assembly since the
meter stick is oriented with the 0 marking above the I meter marking) until the cone
touches the cross bracket. For further increases in U it is necessary to add weights to
the cone assembly.
Previous drop cone penetrometer models measured the diameter of the cone impression. This
was a time consuming operation and restricted the experimenters to two or three drops per
determination of U. Using the construction and procedure described above enables the
operator to quickly make 5 to 10 drops for each determination.
Provision was made for attaching 120, 90, 60, and 45 degree cones to the cone assembly.
Comparative studies of the various cones were set up and the 60 degree cone was finally
selected as most suitable for future studies. Though 120 degree and 90 degree cones gave
consistent results, the diameter of these cones would have to be relatively large to allow
for deep slab penetration. The 45 degree cone was disqualified because of a peculiar
inconsistency; certain snows would fracture around the impact point of this narrow angle
cone.
Analysis of data
As shown in figure 3., a typical run on dry, low density snow, log10 U is a linear
function of log10 Z. This leads to the following expression
U = kZn
where the "n" and"k" are constants evaluated from the log U log Z
plot. Each slab can be described by these constants. It is hypothesized that "n"
and "k" give information pertaining to the mechanical behavior of the slab.
It is useful to reformulate the problem in terms of resistive pressure or hardness. In
Hokkaido, Japan, Yosida and his colleagues, using a free failing measuring system, were
able to determine the resistive force exerted by various types of snow as a function of
time.6 Figure 4. shows their results for freshly deposited snow. From Figure 4.
it appears that the snow compacts beneath a penetrating object and causes the resistive
pressure to increase with depth of penetration. If P represents the resistive pressure of
the snow, then
P = P(Z)
and the total force exerted by the snow on a surface, S, is
The component of R in the z-direction for a 60 degree cone is
The impact energy must perform work
according to
which is the scalar integral
or in differential form
but since U = kzn
and finally solving for P(z)
Mellor5 gives an excellent
summary of previous studies based on similar power relationships between pressure and
penetration. The above relationship is consistent with these studies.
For a slab of thickness H, a single coefficient of hardness P could be defined as
Because the apparatus developed at Alta
gives k and n directly, there seems to be no advantage in using the pressure formulation
constants k1 and n1. However, P will be a useful coefficient to
calculate because it gives ordered hardnesses which can be used to verify the drop cone
theory.
It is possible to think of (k,n) and P as descriptive coefficients of a slab in profile.
If it is realized that the expression U = kzn is only an approximation to the
successive discontinuous collapse of the slab's infinitesimal layers the dimensional
problems inherent in the power function representation can be reconciled.
which is a dimensionally consistent expression. Then as hypothesized in Figure 5., U = kzn
is the approximation to a set of cubic collapse functions, each dimensionally proper.
The results of the 1967 drop cone experiments are shown in Table 1.
Conclusions
The results shown in Table 1. cover only the concluding months of one avalanche season.
Much more data will be needed before correlations can be worked out between (k,n) and slab
release. It is hoped that eventually (k,n) will fit into a complete factor analysis that
will include the variables of Figure 1. This will entail the development of extensive
"in situ" testing procedures.
The low cost and operational simplicity of the drop cone penetrometer gives it the
potential to become a useful soft slab forecasting instrument. Further studies are
planned.
Figure 1.
The first problem. Structure and property variation in the z-direction.
Figure 2.
The Alta drop cone penetrometer.
Figure 3. Linear
approximation to the data of March 19. Taken at 1500.
Figure 4.
Sketch of an oscillogram showing resistive force as a function
of time. (Reference 5.)
Figure 5.
U = zn is an approximation to a discontinuous function. It is
hypothesized that dimensional consistency is achieved if the discontinuous
function is a set of cubics.
Literature Cited
1. Anisimov, M 1958 Snow and Snow Avalanches. Alta Avalanche Study Center Translation No.
1.
2. Inaho, Y 1941 On the hardness of snow. Seppyo vol. 3, p 343 - 349.
3. Kudo, K. and T. Takahashi 1941 Hardness test of snow. Seppyo vol. 3, p 264 - 270.
4. LaChapelle, E. 1966 The relation of crystal riming to avalanche formation in new snow.
Alta Avalanche Study Center. Project B. Progress report no. 1.
5. Mellor, M. 1964 Properties of Snow. Cold Regions Research Engineering Laboratory Ill -
A1
6. Yosida, Z. 1957 Physical Studies on deposited snow. III Mechanical Properties (2)
Contributions from the institute of Low Temperature Science.
