Introduction
The snow resistograph (Fig. 1) is a field instrument designed for the rapid in situ measurement of snow strength. It consists of a probe with a horizontal bit at the bottom. The probe is pushed vertically down to the base of the snowpack, rotated 90 deg., and withdrawn. The resistance to upward movement encountered by the bit is balanced by a spring in the handle and thereby transmitted to a scribe. The rise and fall of the scribe is recorded on a roll of paper unwinding at a rate controlled by the rate of withdrawal of the probe. The graph (resistogram) thus produced shows resistance as a function of snow depth. On the assumption that the force necessary to move the bit upward is essentially the same as the force required to break the snow at that depth, the graph becomes a strength profile (except in the 10 cm disturbed portion at the base of the pack). The working scale for the resistograms is derived by dividing the force in grams by the area of the top silhouette of the bit in cm2.
Fig. 1. The snow resistograph. Assembled instrument (left); recording head (top right); resistance bit (bottom right).
Variations in the rate of withdrawal, of course produce variations in the resistogram. Too rapid a rate introduces a momentum error, while too slow a rate allows compaction of snow ahead of the blade which in turn introduces spurious oscillations and the recording of “false crusts”. Trial and error indicates that a withdrawal rate of 10 cm/s is about optimum. Consistency of withdrawal at this rate produces quite consistent results (Reference BradleyBradley, 1966).
The success of the snow resistograph used in conjunction with the Federal snow sampling tube to evaluate collapsing conditions in the snow-pack (Reference Bradley, Bowles and ŌuraBradley and Bowles, 1967) suggests that either both instruments are delivering reasonably accurate measurements, or that consistent errors in the two instruments tend to cancel each other.
Reference WorkWork (1964) shows that the standard Federal snow sampler tends to overmeasure on the average 7 per cent and up to 12 per cent in very deep snow. Reference Keeler and WeeksKeeler and Weeks (1967) concluded that the resistograph, when compared to the torque shear vane, is responsible for inconsistencies up to a factor ten in its normal working range of 50–1400 g/cm2. These discrepancies underline the need for testing resistograms against some more direct measurements of snow strength. However, this is not an easy matter. The instrument is designed to measure snow so weak that a sample cannot be detached and stressed in the usual way.
LaChapelle (personal communication in 1965) suggested a field test which looked promising:
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Select a site with a snow-pack which possesses a weak basal layer.
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Place a plywood template of suitable area flat on the snow surface and with a thin blade cut the snow vertically down to the ground around the template.
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Leaving the template in place as a platform, apply load to it until the basal snow collapses.
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Calculate compressive strength from the total load applied and area of the template according to the equation
General Plan
On 15 April 1967 ideal conditions for such a test were discovered in meadows along the Gallatin River in Yellowstone Park. Preliminary resistograms showed a very weak basal layer in an otherwise strong snow-pack having depths ranging from 50–150 cm. Snow columns cut with a saw to a cross-sectional area of approximately 1000 cm2 generally collapsed under the weight of a man.
Two tests were conducted—one on 16 April and the other on 23 April—in a snow-pack essentially isothermal at 0°C. General procedure followed LaChapelle’s suggestion. After the column was cut, an initial dead load was placed on the template. The top element of this dead load was a Borg household scale on which human weight was gradually added to produce the collapse within the limit of the scale (250 lb = 114 kg). if the column did not collapse within this limit, more dead weight was added and a new trial was made on the column.
For this procedure the working equation thus becomes
where σ C is the compressive strength (g/cm2), λ the existing snow load on the basal layer as determined by a snow sampling tube (g/cm2), i the initial dead weight (g), x the added weight recorded on the household scale at the time collapse (converted to g), and A the area of the template (cm2). For comparison σ R is the minimum basal snow strength as taken from resistograms (Fig. 2).
Fig. 2. Representative resistograms from Test 1 (top) and Test 2 (bottom).
Discussion
The resistograph is strictly a field instrument. The intent of this in situ test was, of course, to duplicate as nearly as possible the standard laboratory test for compressional strength without disturbing or abandoning the field situation. In addition, the method is apropos in that it tests very directly the theory of snow-pack collapse which lies back of our deep slab avalanche investigations at Montana State University.
Basic to standard compressive strength tests is a standard ratio of cross-sectional area to length of the block to be tested. This aspect was disregarded here in part because of the practical problem of load transport and application and in part because the weak layer to be tested is nearly impossible to define in terms of length. Almost surely when the load exceeds the strength of the weakest zone snow collapse is initiated and thereafter cascades dynamically of its own momentum involving more and more of the column until equilibrium is restored. The “weakest zone” may have essentially no depth or at best a highly variable depth (see Fig. 2).
Three assumptions are associated with the purpose of the saw cut which detaches the snow column:
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The strong upper part of the snow column will be free to move vertically like a piston along frictionless planes.
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The saw does not disturb the weak zone.
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The confining forces on the very friable porous weak layer are essentially zero and the test is hence for unconfined compressive strength.
Obviously, these assumptions are not entirely valid. However, under the actual working conditions which were encountered it is probable that error from these sources was no greater than errors from other sources.
Test I, 15 April, Meadow near Specimen Creek Junction (Table I)
The template used was a nearly square piece of plywood selected at random from a scrap pile. Its area was 1320 cm2. Since the snow was only about 65 cm deep, a carpenter’s saw was satisfactory for cutting the snow. After the saw cut, the household scale was placed on the template. My assistant (Mrs Bradley) eased her weight onto the scale while I watched the dial up to the moment of collapse. Because of unsteadiness the method contained a probable error of ±2 kg.
Collapse when it came was very sudden and amounted to a drop of 10–20 cm.
Fourteen resistograms (Fig. 2) were also taken randomly in the same general area of the meadow. Resistograms carry a hysteresis variability of about +15 g/cm2. Except in the very lowest range the resistograms were usually read to the nearest 50 g/cm2.
Snow load λ for the test was calculated at 20 g/cm2 from the average of six sampling tube cores to the nearest 0.5 g/cm2. These ranged from 16.5 g/cm2 to 21.5 g/cm2.
Initial dead weight i consisted of the combined weight of the scales and template and was approximately 3 kg. All figures for Table I were taken to the nearest whole number. In the last three test blocks, collapse occurred after the maximum reading on the scale was passed. In these x is estimated by extrapolation.
Table I. Comparative Snow Strength Measurements for Test 1 at Specimen Creek, Yellowstone Park, 16 April 1967. σ C = (i+x)A −1+λ Where λ = 20 g/cm2, i = 3 kg, x is the Weight Added to Produce Collapse, A = 1320cm2, σ C is Minimum Compressive Snow Strength, and σ R Minimum Snow Strength as Measured by the Resistograph
Results
The fourteen compressive tests showed a minimum basal snow strength ranging between 43–100 g/cm2 with an average of 85 g/cm2. The resistograms showed a range of from 25–250 g/cm2 with an average of 86 g/cm2. The wider range of resistograms is to be expected since the blade area of the instrument (6.5 cm2 as compared to the template area of 1320 cm2) would be much more sensitive to small-scale variations of the snow-pack. The very close agreement of the two averages is, of course, somewhat fortuitous.
Test 2, 23 April, Meadows near Grayling Pass (Table III)
Certain refinements over Test I were introduced into Test 2:
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By way of simplification a template was constructed with an area of 453 cm2 which permits direct numerical conversion from pounds of weight to load in g/cm2.
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The individual blocks were spaced one meter apart in a straight east–west line across the meadow with each resistogram taken 50 cm south of each compression test (Fig. 3). The intent here was to get a more direct comparison of each test block with adjacent resistograph measurement.
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Snow load λ was obtained by coring the center of each collapsed block thereby giving λ specific to that block.
Fig. 3. Perspective diagram illustrating schematic arrangement for Test 2.
The area was selected because preliminary resistograms showed that the snow-pack possessed a basal snow strength in a higher range but overlapping with that of Test Site 1. Snow depth was about 100 cm which necessitated the use of a one-man woodcutter’s cross-cut saw. In addition, the deeper snow required a double cut to be made on each side of the block because preliminary testing revealed that friction on the sides of the snow block tended to impart significant spurious resistance to collapse.
Initial dead weights i were developed from local materials organized into the units as shown in Table II and applied in the sequence indicated. The household scale, of course, was placed on top of the load and body weight x added to produce collapse.
Table II. Dead Loads i Used in Test 2. Weight in lb on Template with an Area of 453 cm2 is Numerically Equal to Load in g/cm2
Thirteen blocks were tested. In blocks 4 and 5 the snow collapsed just after x reached scale limit (114 kg). Block 8 collapsed as the flagstone was being deposited and before the scale had been added. The loads in these three cases, of course, are estimated by interpolation. Also, resistogram 5 did not reach bottom. The blade hit sagebrush and therefore the basal measurement may not show true minimum strength. Table III details the results of measurement and calculation. Fig. 4 compares the two methods. Figure 2 shows three typical resistograms.
Table III. Comparison of Snow Strength Measurements for Test II at Grayling Pass, Yellowstone Park, 23 April 1967. Compressive Strength
σ C = (i+x)A −1+λ Where A = 453 cm2 (See Table I)
Fig. 4. Comparison of σ C and σ R with respect to position.
Results
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The thirteen compressive tests revealed a basal snow strength which ranged from 166–484 g/cm2 and had an average strength of 322 g/cm2. The thirteen resistograms showed the range to be from 100–400 g/cm2 with an average of 273 g/cm2. Both methods gave about the same general spread with the resistograph recording somewhat lower strength values. It should be recalled here that in comparison with Test 1 the blocks of Test 2 are much longer and narrower. In spite of the double saw cuts it is likely that this discrepancy can be explained in part by additional friction on the sides of the test blocks which had to be overcome by additional load.
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The lack of systematic strength trends in either the compressive tests or the resistograms (Fig. 4) indicates that the variability in basal snow strength exists at some scale less than the one meter spacing between the blocks, and rules out any meaningful correlation between each σ C and adjacent σ R.
Conclusion
On the basis of these two comparative tests it appears that the resistograph provides in situ measurements roughly equivalent to the crushing strength of snow in the range 25–400 g/cm2 at temperatures close to 0°C.
Though desirable, from a practical standpoint it would be quite difficult to continue the LaChapelle test into the upper ranges of the resistograph (400–1400 g/cm2). It is doubtful if the area of the template should be reduced any further. This makes for very difficult load manipulation. It can be said here that with instruments like the resistograph and the torque shear vane, of necessity, a certain amount of “art” goes into measurement taking. The operator’s actions will, to a certain extent, depend upon the “feel” of things. The whole feel of the resistograph as it comes up through the snow-pack suggests to this operator that readings in excess of 1000 g/cm2 may carry considerable error. Up to approximately this point the blade moves through the snow quite smoothly. In these upper ranges, however, the blade, as designed, tends to stop and then break through setting up oscillations very difficult to control by hand. However, in terms of the avalanche problem for which the resistograph was designed we have already reached a practical limit.
Our original hypothesis (Reference BradleyBradley, 1966) states that deep slab avalanches may be initiated by collapse of the weak basal layer under the weight of the overlying snowpack. The strength–load ratio at the base of the pack is used as an index of systemic weakness with a ratio of 1.0 being the theoretical minimum.
The resistograph is used to measure the strength and the snow sampling tube is used to obtain load. In four years of study with these instruments, collapse has been observed only when the basal strength–load ratio was less than 2.0 and greater than 1.0. When the ratio is greater than 4.0 the snow-pack appears to be very stable even when explosive charges are used.
Assuming a basal snow strength of 400 g/cm2 and a greater than average snow density (0.4 g/cm3) it would take at least 5 m of snow to produce collapsing conditions. 2.5 m of snow is about the normal maximum for the Bridger Range of Montana and is the current maximum length of the resistograph shaft. Within the above limits, then, we conclude at this time that the general usefulness and accuracy of the snow resistograph has for practical purposes been demonstrated.
Acknowledgements
I am especially indebted to Mr Edward LaChapelle of the Department of Atmospheric Sciences, University of Washington, for suggesting this very simple and direct solution to an otherwise difficult testing problem. I also wish to thank Messrs Dodge, Scheer, and Martin of the Civil Engineering Department at Montana State University who reviewed the test results and made helpful suggestions. This work is supported by the National Science Foundation under grant CA-756.
