Short Note on Slab-Avalanche Measurements

Abstract

From a study of 205 slab avalanches it is concluded that failure initiates where the slope is 25° or steeper, that slab failure stress is in the range 10²N m^-2 to 10⁴N m^-2, and that the slab failure plane is most commonly at a temperature of -5°C or warmer. The study also indicates that the shear strength of weak layers varies approximately as the square of the density.

Résumé

A partir de l'étude de 205 avalanches de plaque, on conclut que la rupture se produit là où la pente est de 25° ou plus forte, que l'effort au moment de la rupture de la plaque est de l'ordre de 10²N/m²à 10⁴N/m² et que le plan de la rupture de plaque est le plus souvent à une température égale ou supérieure à —5°C. L'étude montre aussi que la résistance au cisaillement des niveaux faibles varie approximativement comme le carré de la densité.

Zusammenfassung

Aus der Untersuchung von 205 Schneebrettlawinen ergibt sich, dass der Bruch bei Hangneigungen von 25° oder mehr eintritt, dass die Bruchspannung zwischen 10²N m^-2und 10⁴N m^-2 liegt und dass die Bruchfläche meistens eine Temperatur von —5°C oder mehr besitzt. Die Studie zeigt weiter, dass die Scherfestigkeit weicher Schichten sich annähernd mit dem Quadrat der Dichte verändert.

Table I gives results from a recent study (Perla, 1977) of 205 cases of snow-slab failure observed in Switzerland, U.S.A., Canada, and Japan. With reference to Figure 1 , the parameters of Table I are explained as follows:

• θ, inclination of the bed-surface, typically measured immediately below the crown,

• h, slab thickness, measured at the crown centre,

• ρ, mean slab density over the thickness h,

• B_xz, the approximate shear stress at the bed-surface prior to failure, computed from ρgh sin θ,

• ρB, density at the bed surface, typically measured by weighing a 50 mm diameter sample,

• T _B, temperature at the bed surface, typically measured in a pit excavated back into the crown.

Fig. 1. Slab avalanche nomenclature and coordinate system.

Table I. Summary of Slab Measurements

The statistics of Table I are probably biased by two factors: First, the samples were taken on accessible slopes; and second, on a given sample day, the observer tended to sample the thicker slabs as opposed to smaller, more innocuous or less spectacular slabs. As a consequence of these factors, it is likely that the sample mean of θ is shifted to a lower value than the population mean, and it is almost certain that the sample mean of h is shifted toward a higher value. A third bias is that wet slabs were not included in proportion to their occurrence since the observations were mostly taken during winter and early spring; only 7 of the 205 observations were taken after 31 March. Thus, the sample mean of T _B is probably shifted to a colder value than the population mean. Lastly, it is possible that 50 mm density samples sometimes over-estimate ρB, especially when failure occurs in a thin, weak layer.

Assuming that the slabs fail at stress B_xz it is possible to find an approximate relationship for the shear strength of bed-surface layers versus bed-surface density ρ B. Figure 2 is a scatter plot of 72 observations of B_xz versus ρB. A power-law fit (r= 0.81) to the data of Figure 2 is

(1)

Equation (1) is subject to the possible bias in ρB. Perhaps a curve-fit based on data obtained with thin, oval density tubes would show an increase in the exponent (larger than 2.06).

Fig. 2. Shear stress at bed surface B_xz versus bed surface density P B, 72 cases.

Taking into account the above biases and limitations of the study, it is nevertheless possible to conclude :

Less than 1% of all slab avalanches initiate where the slope angle is less than 25°.

Less than 5% of all slab avalanches initiate where the slope angle is less than 30°.

The average shear stress at the bed surface prior to failure is in the range of 10²N m^-2 to 10⁴N m^-2.

The most prevalent bed-surface temperature is in the band -5°C to 0°C.

Over 95% of all slab avalanches have a bed-surface temperature of -10°C or warmer.

The shear strength at the bed surface has a large variance as a function of density, but on the average varies approximately as the square of the density.