Introduction

Slab avalanches begin with the shear failure of a weak snowpack layer (Reference McClung,McClung, 1987) and the rutschblock was first used by the Swiss army in the 1960s (Reference Föhn,Föhn, 1987a) to identify such critically weak snowpack layers. Reference Föhn,Föhn (1987a) proposed an interpretation of rutschblock scores in terms of slab stability for skiers, based on a comparison of rutschblock scores with nearby slab avalanching and with adjacent shear-frame stability indices.

In spite of the promise shown by the rutschblock test, its use was limited by the time each test required and by the recommended minimum slope inclination (>30°) — which can compromise operator safety. During the winters of 1990–92 in the Cariboo and Monashee Mountains of western Canada, we investigated potentially faster methods of performing the rutschblock test and the effect of slope inclination on rutschblock scores. Also, we studied the natural variability of rutschblock scores on uniform slopes to determine the precision of one or two tests repeated on a particular slope.

Rutschblock Technique

Test sites for rutschblocks should have an undisturbed snowpack that is representative of the avalanche terrain to be assessed and should be at least 5 m from trees to reduce the effect of inconsistent snow layering near trees.

A pit at least as deep as any potential failure planes, often 1–1.5 m deep, is excavated with a shovel Fig. 1. The wall of the pit that faces down-slope is extended by shovelling until it is at least 2 m across the slope. The sides of the block can be either cut or shovelled, the latter method requiring more time. If the sides of the block are to be shovelled, then two 1.5 m long parallel marks extending up the slope from the pit wall and 2 m apart are made on the snow surface with a ski or ruler. After shovelling trenches just outside these marks, the upper wall is cut with the tail of a ski or a cord.

Fig. 1. Displaced rutschblock caused by skier loading.

If the side walls are to be cut with a ski, ski pole, cord or saw, then the marks for the side walls are 2.1 m apart at the pit wall and 1.9 m apart at the up-slope end of the marks Fig. 2. This flaring of the block reduces the potential for friction at the sides of the block that could affect the rutschblock score.

Fig. 2. Cord-cut rutschblock. Flaring the width of the block from 1.9 to 2.1 m is also used for other techniques that result in narrow side cuts such as saw-, pole-and ski-cut rutschblocks.

After the side walls are cut with a ski pole, saw or the tail of a ski, then the upper wall is cut by the same method. However, if a cord is used, then the side walls and upper wall can be cut simultaneously by extending the cord from the pit, up one side of the block dimensions, around ski poles or avalanche probes at the upper corners and down the other side to the pit (Fig. 2). Two operators in the pit, one holding either end of the cord, alternately pull their end of the cord to “saw” both side walls and the upper wall. An 8 m length of 4–6 mm cord with simple knots tied every 0.3 m successfully cut a wide variety of snow layers except for melt-freeze crusts of ”knife” hardness (Reference Colbeck,Colbeck and others, 1990). This cord-cutting technique produces a rectangular block unlike the method used for the “rutschkeil” test (Reference Munter,Munter, 1991, p. 95–96) that produces a triangular block.

For the saw-cut rutschblocks, a 1.3 m long saw of 3.2 mm aluminum is used to cut the sides and upper wall while standing outside the dimensions of the block. The saw cuts a 10 mm gap in hard snow because of the offset teeth. Most of our saws were jointed so that the saws could be easily carried by skiers with backpacks.

Number of Tests Required to Approximate Median Rutschblock Score

Avalanche workers and ski guides use slope tests such as rutschblocks, explosive tests and test skiing along with observations of avalanches, the snowpack and the weather to assess slab stability. When rutschblocks are used, typically only one or two tests are done to complement the information from other tests and observations.

To determine the number of tests required to approximate the median rutschblock score for a particular slope, we investigated the natural variability of rutschblock scores on uniform slopes. We selected sets of rutschblocks from the data collected during the winters of 1991 and 1992 based on the following criteria:

There were six sets that met these criteria and the distribution of rutschbloc.k scores for these sets are summarized inTable 1 and shown in Figure 3.

Table 1. Frequency distributions of rutschblock scores

Fig. 3. Frequency distributions for six sets of rutschblock scores from uniform slopes.

Mean inclinations for the six sets ranged from 28° to 33°. Within each set, tests were typically 0.3–0.5 m apart in the cross-slope direction and 1 m apart in the up-slope direction. Two of the six sets (6 March 1991 and 7 April 1992) involved two operators of similar weight and the other four sets involved only one operator.

Median rutschblock scores for the six slopes ranged from 3 to 5. This range of median rutschblock scores is appropriate for two reasons. First, the frequency distributions for slopes with median rutschblock scores of 1, 2, 6 or 7 would be truncated by the limits of 1 and 7 that are inherent to rutschblock scores. Secondly, rutschblock precision is of greatest interest for scores in the 3–5 range, since slopes with a higher median score (6 or 7) are generally stable and those slopes with a lower median score (1 or 2) are clearly unstable— safety prevented us from testing any slopes with a median score of 1 or 2 and a mean slope inclination of at least 28°.

The combined frequency distribution of the deviations from the median for the six sets of rutschblocks introduced in Table 1 and Figure 3 are shown in Figure 4. Since rutschblock scores are confined to the range 1–7, a median of 3 does not permit a deviation of +3 and a median of 5 does not permit a deviation of +3. Nevertheless, deviations of +3 were possible for four of the six sets and deviations of −3 were possible for five of the six sets, but neither occurred in 277 tests. This indicates that, on uniform slopes, rutschblock scores that deviate by ±3 from the median are very rare. Indeed, only about 3% of the total results deviate from the median by more than ± 1 as shown in Figure 4.

Fig. 4. Combined distribution of deviations from the median for the six sets of rutschblocks summarized in Table 1.

By assuming the frequency distribution of the deviations shown in Figure 4 are representative of uniform slopes, the probability of a single rutschblock score or median of two scores being within one step of the slope median can be estimated. For the deviations of−2, −1, 0, +1 and +2, the probabilities P₋₂, P−1 P₀, P₊₁, P+2 are 0.007, 0.181, 0.668, 0.123 and 0.022, respectively. The probability of one test giving the median rutschblock score is approximately P ₀ = 0.67. The probability of the result of one test being within one step of the slope median is

The probability of the median of two independent tests being within one-half step of the slope median is

or being within one step of the slope median is 0.99.

Although clusters of low or high rutschblock scores indicative of deficit or pinned areas (Reference Conway, and Abrahamson,Conway and Abrahamson, 1984, Reference Conway, and Abrahamson,1988; Reference Föhn,Föhn, 1989) have not been reported in the literature, we believe that two independent tests should be more than 10 m apart to avoid the possibility of both tests being within a deficit or pinned area.

Although one or two tests appear to provide a useful estimate of the median for a uniform slope, greater variability, and hence reduced precision, is expected at sites that vary by more than ±4° from the mean slope inclination. In particular, we have observed increased variability of rutschblock scores near the top of a slope where wind action distributes snowfall unevenly and where changes in slope inclination can have considerable effect on absorbed solar radiation and consequently snow stratigraphy.

These approaches to the precision of one or two tests must be regarded with caution, since the stability of a snow slope may be more closely related to minimum rutschblock scores. Such minimum scores might indicate a weak zone or deficit area (Reference Conway, and Abrahamson,Conway and Abrahamson, 1984; Reference Föhn,Föhn, 1989) capable of initiating slab failure.

Variations of Rutschblock Technique

Reference Föhn,Föhn (1987a) reported that 20–30 min were required to prepare a rutschblock 1–1.5 m deep by shovelling the lower wall and both sides before cutting the upper wall with a cord. We evaluated two faster techniques in which the sides and upper wall are cut with a cord or a 1.3 m long saw.

The relatively narrow gaps (4–10 mm) on both sides of a block that is cut by cords or saws could possibly result in higher scores because of friction or rapid bonding caused by snow falling into the gaps. For this reason, we used slightly trapezoidal rutschblocks, approximately 1.9 m wide at the upper wall and 2.1 m wide at the lower wall Fig-2.

Average time requirements for two experienced operators to perform a 1–1.3 m deep rutschblock test for various methods of isolating the block are given in Table 2. These times include marking out the block on the surface of the snow, isolating and testing the block but not selecting the site, preparing equipment or making observations of the slab or weak layer. Saw-cut rutschblocks required approximately half as much time as shovelled or cord-cut rutschblocks but saw-cut rutschblocks dictate that a saw weighing 1.2–1.8 kg be carried to the test slope.

Table 2. Time required for two persons for various rutschblock techniques

Although ski-cut rutschblocks can be done without specialized equipment and almost as quickly as saw-cut rutschblocks, their usefulness is limited by the depth of cut that is practical. In hard snow, the bindings for the ski boots limit the depth of cut and hence the effective depth of the test, to approximately 0.6 m. Also, melt–freeze crusts are difficult to cut with a ski.

To investigate a possible effect of the narrow side gaps on rutschblock scores, six saw-cut rutschblocks and 15 cord-cut rutschblocks were each paired with the closest shovelled rutschblock — usually less than 3 m away — that failed on the same weak layer on the same slope. Matching tests were usually completed with 1–2 h of each other.

There was no average difference between the saw-cut tests and their matching shovelled tests (Table 3). Differences between cord-cut tests and their matching shovelled tests averaged 0.5 rutschblock steps. Using a t-test for normally distributed data and a Wilcoxon test that requires only ordinal data, the difference in scores between matched tests is not significant at the 90% level as shown in Table 3. Hence, we were unable to separate any effect of side friction due to saw-or cord-cutting from natural variability of rutschblock scores.

Table 3. Effect of narrow side cuts on rutschblock score

Minimum Slope Inclination for Rutschblocks

Reference Föhn,Föhn (1987a) recommended slopes of at least 30° for rutschblocks which requires that the test be done on inclinations steep enough to produce avalanches. Since dry-slab avalanches are quite rare on slopes of less than 30° and very rare on slopes of less than 25°, we performed rutschblocks on slopes of less than 30° to determine a minimum slope inclination. Our study of the minimum slope inclination for rutschblocks, and of the effect of slope inclination on rutschblock score, requires a shear-frame stability index that we denote by S_s. The following derivation of S_s follows that of Reference Föhn,Föhn (1987b).

Slab failure is believed to begin when the shear strength of a buried weak layer Σ_s is less than the slope parallel shear stress σ_xz in the buried weak layer due to the weight of the overlying slab. (The slope-parallel and slope-perpendicular axes are denoted by x and z respectively.) Accordingly, Reference Roch,Roch (1966a) used the ratio of Σ_s to σ_xz as a stability index for natural avalanches

From statics, the shear stress σ_xz due to the overlying slab of mean density ρ and thickness (measured vertically) h on a slope of angle β from the horizontal is pgh sinβ cosβ in which g is the acceleration due to gravity.

The shear strength of a large area is less than that obtained using a small shear frame, because of the greater probability of a weakness or flaw within the larger area. Accordingly, Reference Föhn,Föhn (1987b) modified Equation (1) by replacing Σ_t by the reduced strength of a large area (>lm²) denoted here by For the 0.025 m² frames that we used, the size effect is given by (Reference Sommerfeld,Sommerfeld, 1980; Reference Föhn,Föhn, 1987b).

Shear strength corrected for normal load is where is the normal load and ϕ is the angle of “internal friction”. However, Reference Mellor,Mellor (1975) questioned the merit of the correction and Reference Roch,Roch’s (1966b) empirical corrections are dependent on the type of snow grains. Nevertheless, an increase in shear strength — as measured by a shear frame — with normal load has been reported by Reference Roch,Roch (1966b) and Reference Perla, and Beck,Perla and Beck (1983). Consistent with Reference Föhn,Föhn (1987b) and Reference Roch,Roch (1966a), we use Reference Roch,Roch’s (1966b) empirical correction for granular snow given by where , is in kPa.

To allow for the stress due to an artificial trigger such as a climber, skier, Snowcat or explosive, Reference Föhn,Föhn (1987b) added an incremental stress term Δσ_xz in the denominator of Equation (1). For a hypothetical skier, the stability index is

For a hypothetical skier on a 30° slope, Reference Föhn,Föhn’s (1987b) formula for Δσ_xz simplifies to 0.13/h kPa where h is in m. Since the derivation assumes snow is a linear elastic isotropic medium and neglects dynamic effects and ski penetration, the expression for Δσ_xz only provides an order-of-magnitude estimation for the incremental shear stress due to a skier.

Reference Föhn,Föhn’s (1987b) data suggest that slopes are often unstable for skiers when S_s ≤ 1, marginally stable when 1 < S_s ;≤ 1.5 and usually stable when S_s > 1.5.

In Figure 5, values of S_s are plotted against median rutschblock scores obtained for the same weak layer from rutschblock tests made within 3 m of the shear-frame tests on the same day.

Fig. 5. Relation between S_s and median rutschblock score. Rutschblock tests for which the load pgh <0.4 kPa are not valid because the operator’s skis often penetrate through or almost through, the slab.

On slopes where the slab load pgh was less than 0.4 kPa, most values of S_s are lower than values corresponding to pgh ≥ 0.4 kPa and show less correlation with median rutschblock scores. For the soft slabs common in our study area, the operator’s skis penetrate close to <50 mm), or through, the weak layer being tested when pgh 0.4 kPa. Hence, rutschblocks give inconsistent or high scores when the skis penetrate close to, or through, the weak layer being tested.

The data presented in Figure 5 are based on slopes that ranged in inclination from 15° to 42°. The three points that correspond to rutschblock tests done at sites inclined at 15–18° are outliers which, given their values of S_s, have surprisingly low rutschblock scores. We suspect that Equation (2), which is based on shear failure, may not be representative of the rutschblock failures that occur on such low-inclination slopes. Until there are more results for slopes of less than 20°, we prefer to use rutschblocks on such low inclination slopes only to find weak layers and not for evaluating slab stability.

In Figure 5, there are 72 points based on rutschblock tests for which β≥ 20° and pgh≥ 0.4 kPa. Although Reference Föhn,Föhn (1987a) used a second-order regression equation to relate rutschblock scores to S_s, we use a simple linear equation since the relationship is purely empirical and because the variability of the points in Figure 5 does not justify a higher-order regression equation. The regression equation between S_s and the median rutschblock score

has a correlation coefficient of r = 0.74 (significance level 0.99).

Except for a median rutschblock score of 6, each of these mean values of S_s shown in Figure 5 is greater than the mean value for the lower rutschblock scores. This anomaly is not surprising, since all the points for R= 6 are based on the “soft-slab” variation of the sixth loading step, which involves repeated jumping on the same compacted spot. (The “hard-slab” variation —jumping without skis — was not suitable in our study area, since it allowed the operator’s boots to penetrate completely through many of the slabs we tested.) While the soft-slab variation of the sixth loading step may not generate more shear stress than the fifth step, it is possible that R = 6 may indicate greater stability than R = 5, because R = 6 indicates that the block did not fail at the fifth loading step and because it is unclear whether S_s or R is a better indicator of slab stability. Nevertheless, the soft-slab variation of the sixth loading step is not ideal, since it apparently does not cause more shear stress than the fifth step.

Effect of Slope Inclination on Rutschblock Score

To study the effect of slope inclination on rutschblock scores, we selected 24 sets of four or more rutschblocks from data collected during the winters of 1991 and 1992 based on the following criteria:

An example of such a set is shown in Figure 6. For the 27 tests, the slope inclination varied from 15° to 44° and the rutschblock scores varied from 2 to 6. In spite of the variability shown in Figure 6, there is a general trend for rutschblock scores to increase as slope inclination decreases.

Fig. 6. Rutschblock scores for 27 rutschblock tests completed on a 16–44° slope on 13 March 1991. In spite of considerable variability, these data show a tendency for rutschblock scores to increase for a decrease in slope inclination.

The effect of slope inclination β on rutschblock score R is assessed in terms of Δβ/ AR, which is the reciprocal of the slope of a straight line fitted to the data by least squares. For any given set of rutschblock scores from a particular slope, Δβ/AR is the average change in slope inclination associated with a one-step increase in rutschblock score.

The correlation between R and β is assessed with the gamma correlation from non-parametric statistics that is suited to rutschblock scores which are ordinal and often involve ties (Reference Siegel, and Castellan,Siegel and Castellan, 1988, p. 291). For the data shown in Figure 6, the gamma correlation coefficient is G = –0.34 and there is only a 3% probability (p = 0.03) of getting such a correlation from sampling random data.

For each of the 24 sets of four or more rutschblocks on slopes that varied by at least 8°, the probabilities associated with the correlations are plotted along the abscissa of Figure 7. A separate symbol is used for the 11 sets that involve less than ten tests, since for such small sets the value of p is only a rough estimate (Statsoft, 1991, p. 270). For most sets, p > 0.10, indicating that slope inclination had no significant effect on rutschblock scores. There are three sets for which the gamma correlation between R and β is marginally significant (0.05 < p 0.10) and seven more significant sets (p ≤ 0.05). Therefore, 14 of the 24 sets do not exhibit a significant R-β effect.

Fig. 7. Probabilities associated with gamma correlations between rutschblock score R and slope inclination β. Each point represents four or more tests on a particular slope which ranged in inclination by at least 8°. Ten of the 11 points for which p<0.1 show a one-step increase in rutschblock score for a 5–13° decrease in slope inclination.

The ordinate of Figure 7 shows Δβ/AR. None of the significant sets (p ≤ 0.05) and only one marginally significant set (p = 0.05, Δβ/ΔR = 33°/rutschblock step) have a positive value for Δβ/ΔR. For this point, Δβ/ΔR is 2.8 standard deviations from the average value for ten tests for which p ≤ 0.10. This makes it an outlier according to the modified 3σ test (Reference Lipson, and Sheth,Lipson and Sheth, 1973, p. 91). For the three other sets of marginal significance and for all seven of the significant sets, Δβ/ΔR ranges from −13° to −5° per rutschblock step and averages −9.7° per rutschblock step. Such values indicate that the rutschblock score tended to increase by 1 when the slope inclination decreased by approximately 10°. The relations between R and β for the 11 sets for which p< 0.10, including the outlier, are shown in Figure 8.

Fig. 8. Eleven sets of rutschblock tests which show significant (p ≤ 0.05) or marginally significant (0.05 < p <0.1) slope effects based on gamma correlations between rutschblock score and slope inclination.

An alternative to analyzing the effect of slope inclination based on field measurements (Figs 6, 7 and 8) is an approach based on Equation (3) and on the calculated stresses in Equation (2). Equation (3) provides values of S_s that correspond to median rutschblock scores and the terms σ_zz, σ_xΖ and Δσ_xz in Equation (2) all include slope inclination β which can be adjusted by trial and error to obtain ΔR = 1. However, this approach requires typical values for ρ and Σ_s in Equation (2). We use ρ = 200 kg m^-3 and Σ_s = l.5 pgh, where the latter represents an approximate upper limit for shear strength of weak layers on slopes capable of producing natural slab avalanches (Reference Schleiss, and Schleiss,Schleiss and Schleiss, 1970; Reference Jamieson, and Johnston,Jamieson and Johnston, 1993).

Consider, for example, a rutschblock score of 3 on an inclination of 35°. To obtain S_s = 1.34 which corresponds to R = 3 (Equation (3)) while satisfying Equation (2) and Σ_s = l.5pgh the height of the slab h must be 0.38 m. Fixing this value of h and hence Σ_s, the value of β in σ_zz, σ_xz , and Δσ_xz of Equation (2) has to be adjusted to 23° to obtain the value of S_s = 1.70 that corresponds to R = 4. Calculated decreases in slope inclination from 35° required to increase rutschblock scores by 1 are given in Table 4 for the 2–6 range of rutschblock scores for which Equation (3) is valid. The resulting values of Δβ/ΔR range from −16° to −6° which agree well with the values determined from field measurements.

Table 4. Calculation steps for effect of slope inclination on rutschblock score

Effect of Slope Inclination on Rutsch Block Displacement

After failure of the weak layer below the rutschblock, some blocks slide off the supporting bed surface and fall into the pit; some stop on the bed surface after displacing less than 0.3 m; and a few jam against the walls of the side cuts — usually as a result of slight rotation. The slope inclination for those blocks that arrest on the bed surface without jamming is of interest for assessing the friction between the slab and bed surface. The percentage of blocks that arrest as an apparent result of basal friction is plotted against slope inclination for 827 tests in Figure 9. On slopes of less than 25°, at least 87% of blocks were arrested by basal friction and, on slopes of more than 31°, less than 23% of blocks were arrested by basal friction.For the dry-slab blocks in our study, basal friction appears to be critical on slopes of 25–30°. Occasionally, slabs are reported to fail on slopes of 25–30° but displace less than 0.5 m without releasing a slab avalanche (see photograph on p. 161 of Reference Daffern,Daffern (1992)). Also, in support of this critical range of inclinations, Reference Perla,Perla (1977) reported that at most 5% of all slab avalanches start on slopes of 30° or less and, at most, 1 % of all slab avalanches start on slopes of 25° or less.

Fig. 9. Effect of slope inclination on the percentage of rutschblocks arrested by basal friction.

Block displacements of less than 20 mm are sometimes not noticed by the skier loading the rutschblock. On slopes of less than 30°, rutschblock displacements were 20 mm or less for 118 of 287 tests (41%). Failure to notice displacement can result in an incorrect rutschblock score and, at worst, an overestimation of slab stability. To ensure rutschblock failures are noticed on the earliest loading step, we recommend that the lower wall of the block be cut smoothly and that the displacement be observed by a second person standing near the lower wall, especially on slopes of 30° or less.

Conclusions

The following are the main conclusions reached after three winters of field work involving over 900 rutschblock tests in the Cariboo and Monashee Mountains. During testing in the study areas, the snow was dry, the snowpack depth was rarely less than 2 m and the depth of the active weak layers was rarely more than 1 m.

• 1. On a uniform slope that varies in slope inclination by less than 10°, one rutschblock test has an approximate 67% probability of giving the median score for the slope and 97% probability of giving a score within one step of the slope median. The probability of the median score of two independent tests being within one-half step of the slope median is approximately 91%.

• 2. The time required to perform a rutschblock is reduced by approximately half by using a ski or specialized saw to cut the sides and upper wall of the rutschblock. Provided no knife-hard crusts exist in the slab to be cut, 4–6 mm knotted cords can also be used. These alternative block-cutting techniques do not appear to affect the resulting rutschblock scores.

• 3. The procedure for loading step 6 is not ideal. One method, jumping after removing the skis, did not effectively test most slabs in our study area because the operator’s boots penetrated too deeply. It is doubtful that the alternative method, moving 0.35 m down the block to jump with skis on, effectively increases the incremental shear stress in the weak layer compared to loading step 5.

• 4. The rutschblock test can give erroneously high scores when the operator’s skis penetrate through, or close to (<50 mm), potential failure planes. Failure planes underlying a slab load of less than 0.4 kPa are frequently not tested effectively by the rutschblock test.

• 5. Rutschblock scores from inclinations as low as 20° correlate with the stability index for skier loading 5 g. Rutschblock scores on slopes below 20° are not consistent with the same correlation. Until further studies on such gentle slopes are completed, rutschblock tests on such low-inclination slopes should be used only to locate potential failure planes.

• 6. There is a general tendency for rutschblock scores to increase by one step for each 10° decrease in slope inclination. Such an effect is often obscured by natural variability of rutschblock scores and was only apparent in ten of 24 data sets.

• 7. Rutschblock tests done on slopes of less than 30° require a smooth lower wall and a second person standing in or near the pit to observe the small displacements (less than 20 mm) that indicate a shear failure.