the stability index and various triggering...

Avalanche Formation, Movement and Effects (Proceedings of the Davos Symposium, September 1985). IAHS Publ. no. 162,1987.

The stability index and various triggering mechanisms

PAUL M. B. FÔHN Federal Institute for Snow and Avalanche Research, CH-7260 Weissfluhjoch/Davos, Switzerland

ABSTRACT There is a urgent need among avalanche forecasters, avalanche safety personnel and consultants for more quantitative information on slope instability. This paper describes special shear frame measuring procedures and analytical methods applied to check the validity of a stability index approach. Special attention has been given to the question of extension of the usual index towards common artificial triggering mechanisms to improve its correlation with observed avalanches.

Shear frame series of various sizes indicate that size effects may be present.

A data set of about 110 potential dry slab situations shows that 75 % of all situations are properly described by the index S (natural slab releases) or by S' (artificially triggered slabs). Considering artificial peak stresses in stability calculations definitely improves the predictive potential and yields additional hints about causes of slab releases. The most important demand is to find representative and safe slope spots for measurements. These aspects are discussed in terms of variances and error sources.

L'indice de stabilité et les divers mécanismes de déclenchement RESUME Les prévisionnistes, le personnel de sécurité des pistes et les experts sont intéressés à recevoir plus d'information quantitative quant à la stabilité des pentes. Cet article décrit des essais lors desquels on a mesurés les forces et les résistances au cisaillement dans les couches les plus faibles. L'indice de stabilité de la couverture de neige concernant la rupture au cisaillement est analysé pour des ruptures naturelles et artificielles. Les surcharges artificielles (skieur, explosif etc.) sont estimées par des calculs simples.

Un ensemble de 110 situations avalancheuses montre l'utilité d'une telle approche:. 75 % des cas sont bien classés, c'est-à-dire que l'indice de stabilité S (déclenchements naturels) ou S' (déclenchements artificiels) montre souvent si un déclenchement de plaque est probable ou non. Le problème important du choix des pentes representatives pour de tels essaix est également discuté.

195

196 Paul M. B. Fchn

INTRODUCTION

The search for a concise snow slope stability index has started very early (Bûcher,1948; Krasnosel'skii,1964; Jaccard,1966; Roch, 1966), but only in recent years it has been revived (Sommerfeld et al,1976,1979,1980; Perla,1977,1980,1982; Conway and Abrahamson, 1984). The revival may be explained by improvements in measuring procedures and in statistical evaluation methods, and by the lasting demand to clarify the usefulness of a simple stability index. Sustained by studies of Sommerfeld (1976) and Perla (1977) which showed that a stability index might often explain slab releases, we started a measuring and evaluation program in the late seventies to define an "in situ" stability index.

In fairly regular time intervals the well-known stability index S - taken as the ratio between shear strength and stress in the least stable sublayer - has been evaluated on various slopes. This index has been compared with observed natural or triggered slab avalanches at the same day on similar slopes (same aspect and altitude).

FIELD MEASUREMENTS

It is commonly accepted in snow mechanics (Mellor, 1975; Perla, 1977) that most often locations of minimal shear strength decide if and where macroscopic ruptures occur in a sloping snowpack. Hence for a stability index the shear strength of the least stable sublayer or interface at a representative location has to be measured. Up to now the position of this layer or interface has been found by inspection of concurrent avalanche fracture lines or by a shovel shear test (Sommerfeld, 1984). Because slab crowns are often inaccessible or simply not present and the shovel test does not yield the least stable sublayer (it may be found afterwards by comparison of measured shear frame data), the Rutschblock-method has been introduced. Excavating and separating vertically a snow block of 3 m surface area from the residual sloping snow cover, a skier marching or jumping onto the surface may produce a mini-slab. Assuming that the failure layer is identical with the least stable sublayer, shear frame measurements may be executed on this layer adjacent to the block area, cf. Fohn (1987). Shear frame measurements were usually performed on the left and righthand side of the block area and/or near slab avalanche flanks whenever present. At the same time slope angle, slab layer thickness and density of overburden layers were measured. A sturdy shear frame of 0.05 m area (0.2mx0.25m) with four fins was used for all routine measurements.

Size effects

The shear frame area has - according to initial test series - a definite influence on the results. As reported by Sommerfeld (1976, 1984) and Perla (1977, 1982) shear strength decreases with increasing

The stability index and various triggering mechanisms 197

TABLE 1 Shear index ratios obtained by various frame -areas

large area

2 m

0.05 0.05 0.05 0.1

0.2 0.25

0.2

small area

2 m

0.01 0.025 0.03 0.05

0.05 0.05

0.1

shear index

ratio large/small

1.16 0.93

0.82

0.79

0.88

shear index

ratio large/s mall Sommerfeld, 1980 0.67

0.90 0.89

shear index

ratio large/small Perla, 1982

0.997

0.992

0.803

0.73

frame area. Test series have been carried out with various frame areas. The obtained shear index ratios confirm the reported size effects (Table 1). The ratios are similar to those published by other investigators. Our series, involving the old small 0.01 m frame area, show a mean ratio >1 compared with the new 0.05 m frame. This unexpected result may be due to the difficulty that such a small frame may often not be inserted above weak layers (e.g. surface hoar) without breaking part of the layer. This results in lower shear strength values. With the aid of the published absolute correction factors based on the theory of Daniels (1945) and our own measurements, a curve of the correction factors for various frame areas may be constructed. The correction factor of our standard frame of

0.4

O Id <r CE o o

0.2

< X CO

\<r to CJ

O O d d

o d

ZNo.4-1683

X DANIELS(I945). SOMMERFELD et ol. (1979, 1980, 1984)

v REL. MEAS. PERLA (1977)

A REL. MEAS. FO'HN (1986)

CJ

O

I

0.1 0.2 0.3 SHEAR FRAME AREA [m zJ

FIG. 1 Correction factors for various frame areas.

198 Paul M. B. Fchn

0.05 m amounts to 0.7. It may be noted that the given cury e predicts shear strength for sample areas greater then roughly 0.5 m would not show any size effect.

Effect of stress rate

Measurable rate effects reported in literature (Salm, 1971; Perla, 1977, 1980, 1982; de Montmollin, 1982) have not been observed in alternating series of quick (< 1 sec) and slow shear (5-20 sec) with the 0.05 m frame area.

However if one postulates similarity between the tensile and shear behavior of snow a stress rate effect has to be assumed. Either the fast test with large scatter swamps out this effect or the present measurements cover a semibrittle or brittle range where this effect is of minor importance (McClung, 1986).

Variances

The variance of the strength of alpine snow is relatively large, presumably due to spatial inhomogeneity. The measuring procedures and the poor definition of snow layering are also responsible for variances. It has to be stated that if a weak layer is superposed by an ice layer or a strong crust the shear strength may not be measured by shear frame methods. In order to yield a measure of dispersion for given means,three different test series have been established. Initial measurements with a 0.01 m frame at a level study plot with seemingly homogeneous rather dense snow layers suggest that standard deviations of 18 - 35 % may be expected around the arithmetic mean in this type of snow. The test series are given in table 2.

TABLE 2 Variances on level snow bench with a 0.01 m frame area

No of Shear index [N/m2] samples mean S.D. median Min.

Crystal Density Max. form size kg m

mm cf.UNESC0(l970)

47

52

24

4590

7680

6430

1590 (35%) 2450 (32%) 1160 (18%)

4600

8100

6300

1000 7600

2100 12400

4200 8500

• Q 1/2-1 250

D 1 310

DO 1 - 2 316

A second test series performed in a marked weak layer at an inclined


artificially graded plane showed clearly smaller standard deviations, namely 18 - 23 % of the mean. The data are represented in Table 3.

TABLE 3 Variances at inclined weak layer with a 0.05 m frame area

No of Shear index 2

N/m Crystal samples mean S.D. median Min. Max. form size

mm 23

28

2674

2708

488 (18%) 610

(23%)

2680

2700

1640 3820 n(y) 2

1740 3860 n(y) 2

Finally measurements at and beside the bed surface layer of released slabs or at the failure layer of Rutschblock's demonstrate that the overall standard deviation of 40 series with about 10 measurements each over one winter amounts to 25.4 %. This value may be regarded as representative for in situ measurements with the 0.05 m shear frame.

STABILITY INDEX

The usual stability index S is defined as the ratio of the mean shear strength (f) of the weakest layer to the shear stress component ( T ) parallel to the slope at a given slope location prior 4- X Z • -P • n

to macroscopic failure. Using a coordinate system and notations as shown in Fig. 1

and correcting the measured shear strength c (cohesion) for normal pressure and size effects (cf. FIG. 2) the stability index may be formulated as

X 2 (c+tgto Q ) t x z " j> gh-sin2y

where <p is the internal friction angle of the least stable layer and Q =ygh-cos y/ the normal pressure.

Equation (1) contains the Coulomb-Mohr friction law, which relates shear strength to normal pressure in a linear form. Even if its validity for snow is not well established, this simple relation could not yet be replaced for the solution of practical problems (Mellor, 1975). For plane and slow deformations it seems possible to approximate the shear strength as a linear function of g , at least in the narrow range of our measured normal stresses (150^ g 5 1600 Pa). The tangent of the unknown friction angle was calculated by an empirical relation of Roch (1966): tgy>= 0.4 + 8-10~ c [c in Pa].

It is obvious that this simple index is only valid if certain preconditions are fullfilled or certain assumptions are more or less valid.

(1)

200 Paul M. B. Fôhn

FIG. 2 Slab avalanche coordinate system.

These are: - snow is an isotropic, quasi-elastic medium . - primary failures occur in shear with the weakest link governing the failure process. - the measurements are executed on a uniform, more or less extended slope (neutral zone) where deviatoric stress gradients are of minor importance. - at the time of failure principal stress component t is parallel to T , i.e. the maximum shear

xz stress due to body forces acts along the weakest layer.

Stability index integrating human triggering

Because in a normal winter most slabs causing accidents are triggered by human actions (by skiers, climbers, snowmobiles, explosives, etc.) a stability index integrating these influences is highly desirable. The extended form may be written as

T0 S* =

+^C (2)

T is again the mean shear strength of the weakest layer, -j' is the shear stress due to body forces in this layer and At denotes

XZ

the peak shear stress in this layer due to human actions. This index contains only stress increasing elements and not strength loss due to metamorphism and bond-melting. One may assume that strength loss within hours is of minor importance in these buried layers.

A skier, which is often the main triggering cause, may be approximated by a line load. It is assumed that the skier is crossing the extended, uniform slope along a contour line and that his weight of 85 kg is concentrated on a line, say one ski. Assuming a stress-free surface and elastic behaviour of the snow, the shear stress may be calculated by the stress-functions of Airy (Fbppl, 1947):

2 R , ~Z— cos (oc-/3) sin ex cos ct (3) âr

and i f [3 = 9 0 ° - y

AT Ttr

s i n {d+y) s i n 2oC ( 4 )


R = T = -—z~ = 50 kg m is the specific line load, a constant; I 1.7m

r is the radius-vector of any points of interest in the snowcover, ot the angle between slope and r and fb the complement of the slope angle. The notations are represented on Fig. 3. Because for this purpose the peak shear stress is of main interest, we differentiate Ax in equation (3) with respect to oc to find position and magnitude of this maximum

d(/ÛT ) R xz ?

— J — = - — sin (<*-/3) sin o( + cos (cX- ft) 2 cos 2cX=0 (5)

The value of <X which defines the position of maximum ZIT' is XZ

OC . Typical values of OC for various slope angles are as „ max max follows :

7 35° 38° 45°

I3

55° 52° 45°

a max 47° 46° 45°

The peak shear stress occurs beneath and slightly downslope of the skier and the magnitude is represented in Fig.3. The peak values of At in a weak layer of depth h may be calculated

replacing r = h sin/5 ' sin oc

in equation (3) by:

2 R cos c< max

FIG

• 2 • / sin ot. sin ( ex. max max

y) (6)

Shear stress created by skier.

For a mean or standard slab h = 0.8 m, y = 220 y =338'

kg m ) which has been determined by Fohn (1980) or similarly by Perla (1977) the peak shear stress in the failure layer amounts to about 200 Pa (cf. Fig. 3). A climber, whose weight is sometimes sustained by one foot exerts about twice the shear stress of a skier on layers close to the snowsurface (0.2 s h 0.5 m), but reaches - due to the r decay as a point source - in lower layers (0.8 € h^ 1.5 m) only half the shear stress of a skier.

202 Paul M. B. Fohn

A snowmobile (e.g. Ratrac) is also quite often a triggering source for slabs and may be approximated as a two-dimensional band-load as represented in Fig. 4. Assuming quasi-elastic behaviour, the stress components in direction z and x may be formulated again according to Airy as:

^ x z ( z ) = ^ ( c o s 2 C 2 - c o s 2 a i ]

and

AT (X) xz

- ^ ( oc - oc) 7T 2 r

(7)

- ^ (sin2«2 - sin 2^) (8)

where ex and ex are the two position angles of any point of interest in relation to the band-load of length 1 (cf. Fig.4).

The specific band-load components p and q are represented by:

W cos y 1-b

(9)

q = W sin y 1-b

(10)

where W is the weight of the snowmobile (Ratrac = 5500 kg), Î its length (3.2 m) and b its width reduced to the load bearing crawler tracks (3.3 m).

Summing up the two components, the shear stress due to a two-dimensional band-load may be given by:

(11)

ÛX W t »v Icosy (cos2a--co$2a.)-2sin y (tr -or. J-sin* (sin2<r, -s in2« )>

2-K-ÎV d ' * à 1) Calculating the stress

for the mean slab ( f =38°, h = 0.8 m, y= 220 kg/m ) we get the astonishing result that a snowmobile produces a peak shear stress of roughly 2400 Pa in the failure layer, i.e. more than 10 times the stress produced by a skier. According to numerical calculations by Stocker (1980) this peak shear stress is situated beneath the lower, down-slope end of the snowmobile.

FIG. 4 Snowmobile load and coordinate system.


A comparison of these stress sources and their magnitude with depth is given in Figure 5. There the stress magnitude due to body forces of the overburden slab layers is also represented for a mean slab.

It is obvious that these shear stress-calculations may only represent the order of magnitude of stresses which might act on a failure layer. In addition to these static, gravitational forces, there are dynamic forces which must be considered. Because rapidly moving loads (e.g. skiers) or vibrating loads (e.g. snowmobiles) would generally increase the stress rate and hence the instability, the given values may be regarded as conservative estimates. Before the damping or stress concentrating effects of weak and hard

layers in a snowpack are better known, it makes no sense to include dynamic effects in such model-calculations.

The use of explosives to trigger dry slabs is often applied mainly in skiing areas. Explosive blasts produce elastic and plastic shock waves. Because there is a very strong attenuation of "plastic" waves with distance in snow, the elastic wave has to be taken in consideration. According to Mellor (1977) and Gubler (1977) the peak stress may be approximated by:

FIG. 5

DEPTH OF WEAKEST LAYER h|m]

Comparison of various peak stresses,

AT (X) = a . v(x)- c xz Js s

where p is the mean density of the initial snow, l.

10SX4 100 m (12) »s ' s'

.e. of the slab layers, c the sonic velocity in these layers and v(x) the particle velocity at a distance x from the explosion centre. The sonic velocity of high-winter snow is mainly dependent on snow density and covers the range of 500 - 850 m s . Calculating the vertical particle velocities v(x) by two empirical formulas of Gubler (1977) for 1 kg "Plastif'-explosions, the peak shear stresses may be approximated as a function of x by equations (12) and (13) or (14).

explosion 1 m over snow surface, dry snow

v(x) 0.94 x -1.2

,10 sS x =S 100 m (13)

204 Paul M. B. Fchn

explosion at the snow surface, dry-snow

v(x) 0.56 x -1.2

,10 x é 100 m :i4)

These peak shear stresses have been approximated for various distances x from the explosion centre and the main perturbation areas are -together with the peak shear stresses of a skier and a snowmobile - represented in Table 4. Explosives and snowmobiles create a very large perturbation shear stress on snowlayers, but explosives also have also a large perturbation area.

TABLE 4 Comparison of peak shear stress and substantially stressed areas by various triggering sources at a depth of about 0.5 m beneath surf ace .

Triggering source

Peak shear stress AT at h=0.5 m lxz

Pa

Peak ratio relative to skier

Area, where shear stress >0.5^r

lkg explosion, air, 1 m above snow

lkg explosion at snow surface

snowmobile, "Ratrac"

climber, (point load)

skier (line load)

10

6-10

2.6-10

9-10 2

? 3,5-10

30

17

600

500

10

0.1

CORRELATION OF STABILITY INDICES WITH AVALANCHE ACTIVITY

With the aid of the previously described triggering sources the stability indices (S and S1) have been calculated for 110 potential avalanche situations. Information about the date, measuring location, index values and concurrent avalanches are given in the Appendix. Because snow depth and slope angle are highly variable on an avalanche slope a minimal stability index (S . ) has also been calculated, assuming for the primary fracture zone a slope angle of 45° and twice the snowdepth measured at the pit location.

The efficiency of the approach may be checked by comparing primarily S or S' with concurrent avalanches and the way they were triggered: Situations when either natural or artificially triggered slabs occured, are rated successful, if S (S1) <é 1. Situations when the same happened, but 1.0 < S (S') é 1.5 are called semi-successes (looking at the variances of measured c-values,


this seems justified). Finally rating situations as failures when S (S') >*1.5 and avalanches are observed, we get a success score of 75 %.

This mediocre result may be explained by 3 reasons: (1) It is very difficult to always find representative and

safe measuring locations. In the case of triggered avalanches (30 % of total) the measurements have often been executed 24 hours later, in the meanwhile snow strength may have increased substantially.

(2) Using about 10 shear frame values - covering an area of 1-2 m - mean values of c are used to calculate mean values of S or S'. Primary fractures occur rather at spots where stability is at minimum not at mean.

(3) Because the avalanche observation system was incomplete, the validity or the invalidity of the approach had to be tested by active testing methods: Every slope which has been surveyed by stability measurements, had to be tested by triggering methods with rising stress peaks (use of explosives). It is obvious that such active methods were very expensive, dangerous and time-consuming.

CONCLUSIONS

The extended stability index approach (S or S') has some predictive potential and allows to approximate for 3/4 of all cases the trend in avalanche activity. The special treatment of artificially triggered avalanches improves the score from 55 % to 75 %.

The main deficiency of the method is that the measurements have to be executed at representative slope spots (neutral slope parts) which additionally should be safe. This virtual contradiction may be bypassed by measuring at small or medium sized slopes (length: 30 - 100 m) with suitable terrain. Such restrictions confine the method to experienced teams. Another pending problem, how to find the representative (least stable) layer, could be solved by executing a "Rutschblock" first, which can reveal this layer.

Special series of shear frame measurements show that the values may be fitted by a normal distribution and hence the deciding minimum may be approximated by its mean (X) and variance (s), e.g. X - 2s. 2

The mean standard deviation of shear frame measurements (0.05 m ) over one winter amounts to 25 %. The comparison between shear frames of different size confirms the same sample size effects reported in literature. Stress rate effects could not be observed.

The order of magnitude of peak stresses due to artificial triggering mechanisms (e.g. skiers) may be approximated for an isotopic, linear elastic medium. Such approximations are very useful and allow the comparison of their triggering potential. However due to snowcover layering, dynamic effects and viscous damping, which

206 Paul M. B. Fchn

have not yet considered, the results yield an order of magnitude only. Appropriate stress measurements beneath a skier in a layered snowcover would clarify these points.

Although the stability index approach has several deficiencies, it is now the only method which yields a simultaneous quantitative measure of slab danger and insight into slab forming processes.

ACKNOWLEDGEMENT

I would like to thank Dr. C. Jaccard and R. Meister for discussions and various support. The following made this study possible, mainly through their field work assistence, even in dangerous situations: R. Meister, H.-J. Etter, B. Heinzer, B. Beer, W. Zierhofer, Th. Reinhard, J. Kindschi, B. Regli, J. Planta.

REFERENCES

Bûcher, E. (1948) Beitrag zu den theoretischen Grundlagen des Lawinenverbaus. Beitrage zur Géologie der Schweiz, Geotechnische Série, Hydrologie, Lieferung 6, Kommisionsverlag Kummerly & Frey, Bern, 113 p.

Conway, H. & Abrahamson, J. (1984) Snow stability index, J. of Glac, Vol. 30, No. 106, p. 321 - 27.

Daniels, H.E. (1945) The statistical theory of the strength of bundles of threads. I. Proceedings of the Royal Society of London, Ser. A, Vol. 183, No. 995, p. 405 - 35.

Fohn, P. (1981) Schneefeldsprengungen und Stabilitat der Schnee-decke. Informationsberichte des Bayerischen Landesamtes fur Wasserwirtschaft, Heft 8, p. 51 - 67.

Gubler, H.U. (1978) An alternate statistical interpretation of the strength of snow. J. of Glac, Vol. 20, No. 83, p. 343 -57.

Jaccard, C. (1966) Stabilité des plaques de neige. International Symposium on scientific aspects of snow and ice avalanches, 1965, Davos, AIHS-Publ. No. 69, p. 33-44.

Krasnosel'skii, E.B. (1964) On the problem of determining the degree of avalanche hazard in the high-mountain regions of central Tien Shan. Transactions of the Voyeykov Main Geophysical Observatory (Trudy GG0), No. 150, p. 133 - 139. Translated by Yuri Ksander.

McClung, D.M. (1986) Personal communication Mellor, M. (1975) A review of basic snow mechanics, Snow mechanics

Symposium, Grindelwald, 1974, IAHS-Publication Nr. 114, p. 251 - 291.

Montmollin, V. de (1982) Shear tests on snow explained by fast metamorphism. J. of Glac, Vol. 28, No. 98, p. 187 - 198.

Perla, R. (1977) Slab avalanche measurements, Canadian Geotechnical Journal, Vol. 14, Nr. 2, 1977, p. 206 -213.

Perla, R. (1980) Avalanche release, motion, and impact, from:


Dynamics of snow and ice masses, Editor: Colbeck S., CRREL,

Academic Press, Inc. Perla R, Beck T.M.H. & Cheng T.T. (1982) The shear strength index

of Alpine snow. Cold Regions and Technology, Vol. 6, p. 11 -20.

Roch, A. (1966) Les Variations de la résistance de la neige. IUGG.

Internat. Symposium on scientific aspects of snow and ice avalanches, 1965, AIHS-Publ. No. 69, p. 8 6 - 9 9 .

Salm, B. (1971) On the rheological behavior of snow under high

stresses. Contributions from the Institute of Low Temperature Science, Hokkaido University (Sapporo), Ser. A., No. 23. p.1-43.

Sommerfeld, R.A., King R.M. & Budding F. (1976) A correction factor for Roch1s stability index of slab avalanche release. J. of Glac, Vol. 17, No. 75, p. 145 - 147.

Sommerfeld, R.A. & King, R.M. (1979) A recommandation for the application of the Roch index for slab avalanche release. J. of

Glac, Vol. 22, No. 88, p. 547 - 549. Sommerfeld R.A. (1980) Statistical models of snow strength, J. of

Glac. Vol. 26, No. 94, p. 217 - 223. Sommerfeld, R.A. (1984) Instructions for using the 250 cm shear

frame to evaluate the strength of a buried snow surface. Res.

Note RM-446, USDA Forest Service. Stocker, Th. (1980) Modellrechnungen zu den Spannungsverteilungen

in der Schneedecke verursacht durch Skifahrer und Pistenfahr-

zeuge, Int. Bericht SLF, Nr. 584, 25 p. UNESCO (1970) UNESC0/IASH/WM0, Seasonal Snow Cover. Technical

papers in hydrology, No. 2, UNESCO, Place de Fontenoy, 75 Paris, 38 p.

208 Paul M. B. FÔhn

APPENDIX Snowpack-/avalanche situations sampled during the winters 1980/81 - 1985/86 and the corresponding stability indices: S denotes the natural stability index, S' describes the snowpack stability in the case of artificial triggering. Slope size (S=small, é50 m in length, M=medium 50 - 100 m, L=> 100 m); RB: measurements at Rutschblock-location, A:meas. at avalanche flanks, A': aval, artificially triggered

Date

14.11.80

7/8.12.80

24.12.80

7/8.01.81

22.01.81

22.01.81

27/28.01.81

9.04.81

9.04.81

8.12.81

22.12.81

28.12.81

4/5.01.82

14.01.82

14/15.03.82

25.03.82

1.04.82

8.04.82

20.04.82

9/10.05.82

19.11.82

23.11.82

30.11.82

19/20.12.82

21/22.12.82

13.01.83

13.01.83

15.02.83

16.02.83

18.02.83

ize

m

slo

pe

S L S M S M L M L M S S

L M L S S S S L

S S S L S

S M M M M

-p ai

w

c m

ea

RB A' RB

A RB RB A' RB RB RB RB RB

A' RB

A1

RB RB RB RB A' +

RB

RB RB RB A' A+ RB

RB RB RB RB RB

Stability

Index S

S

4.2 4.1

10.1

3.3 3.5

11.3

2.9 3.4 0.8 1.5 3.0 2.3

2.1 6.2

2.9 2.2 2.0 3.2

7.6

3.6

1.8 13.4

2.9 1.6

1.7

6.0 3.7 3.8 4.6 5.3

S . m m

2.0 1.4 4.6 1.6 1.4 6.6 1.4

1.3 0.6 0.7 1.5 1.0

1.0 2.9 1.5 1.0 0.9 0.8 3.6

1.6

0.8 5.8 1.3 0.8

0.8

2.9 1.8 1.9 2.2

2.6

Stability Index S'

S'

0.8 0.9-1.8

0.2

2.6 0.6 2.5 1.5 2.5 0.6 0.1 1.2 0.5

1.0

0.8 0.9 1.1 1.3 1.5 3.4

2.2

0.8 2.1 0.8 •1.4

1.1

1.7 0.8 1.8 2.1 3.2

Verification of S or

S1 by natural or arti

ficially trig, avalanches

—

9 slabs trig, by explosives

1 slab trig, by explosives

2 nat. slabs

(NE-slope)

(S-slope)

1 slab trig, by 3 skiers

(NW-slope)

2 moist nat. aval.(E-slope)

4 nat. slabs

— slope fractured without

aval. by 1 man stepping on


— 1 slab trig, by 1 skier

1 nat. slab

— — —


marching in a row

several nat. slabs

— —


1 nat. slab + 1 slab trig.

by skier

(N-slope)

(SE-slope)

— —

—


24.02.83 27/28.02.83

3.03.83 3.03.83

3/4.03.83 11.03.83

4/5.04.83 5.04.83 8.04.83 14.12.83

27/28.01.84 3.02.84 23.02.84

4/5.04.84

12.04.84 13.04.84 13.04.84 26.04.84 9.05.84

15.11.84 19.11.84 29.11.84 30.11.84 4.12.84

12/13.12.84 20/21.12.84

28.12.84

10.01.85 10.01.85

15/10.01.85

18.01.85

21.01.85

21/22.01.85

25.01.85

25.01.85

M

L

S S S

s M L

S M L L L L

L M M L L L L L L L L L

L

L M

L

M

L

M

M

L

RB

A'

RB RB

A RB

A' A' RB RB

A' RB RB A'

RB RB RB RB RB RB RB RB

RB RB A1

A'

RB

RB RB

A'

RB

RB

A'

RB

RB

6.0

4.3

6.2

2.8

3.1 13.1 4.0 4.1 7.7 3.2 3.3 19.0 2.2 7.6

3.2 4.3 5.5 5.5 8.0 7.1

6.1 3.7 5.7 4.0 1.7 2.9

2.1

9.6 1.1

1.1

2.2

0.8

1.6

6.4

2.9

2.9 2.1

3.1

1.3 1.5 6.3 1.8 1.7 3.6 1.6 1.6 9.0 1.1 3.7

1.5 2.1 2.7 2.6 3.8 3.4 2.8 1.8 2.7 1.9 0.8 1.0

1.0

4.5 0.5

0.5

1.1

0.4

0.8

3.0

1.4

3.5 2.8

1.9 0.8 1.5

3 1 0

2 1 2 4.8 1.7 1.5

1.8 0.9 2.7 2.8 1.5 0.7 0.4 0.6 2.0 1.4 1.1 -0.6

1.1

2.2 0.2

0.2-0.4

0.8

0.2

0.2-0.5

0.4-1.4

0.3-1.5

0.2-

1 slab trig, by 9 skiers in a row ascending 1 nat. slab (NW-slope)

(SE-slope) 1 nat slab

1 slab by some skiers 1 slab by explosives


3 adjacent slabs trig, by skiers

(NE-slopel (W-slope)


1 slab trig, by 8 skiers 1 slab trig, by explosion 1 slab trig, by skier 1 nat. slab + 1.aval trig, by skier

(NE-slope) 3 nat. slab + 1 slab trig, by skiers (SSW-slope) 3 nat. slab + 4 trig, by skiers, 3 slab trig, by explosions

1 slab trig.

2 slabs trig.

1 nat. slab by 2 skiers 1 nat slabs by skiers

1 nat. slab + 2 slabs trig. by skiers, + 1 slab trig, by explosions 2 slabs trig, by (SSW-slope) skiers + 1 slab trig. by explosives 1 nat. slab + (NE-slope) 1 slab trig, by skiers + 4 slabs trig, by explosives

210 Paul M. B. FÔhn

28.01.85 29.01.85

31.01.85

31.01.85 3/4.02.85

5.02.85

5.02.85

5.02.85 7.02.85 13.02.85 13.02.85

20.02.85 22.02.85 7.03.85 14.03.85 14.03.85 29.03./

1.04.85 30.03./ 1.04.85

3/4.04.85

13.04.85

18/19.04.85

18/19.04.85

2.04.85 4.05.85 16.11.85 18.12.85 23.12.85 30.12.85

30.12.85 7.01.86

16.01.86 21.01.86

M A' M RB

S RB

L RB L A' S RB

M A

S RB L A' M RB L A'

L RB M RB S RB M RB M RB

L A'

L A' L A'

L RB

L A'

L A'

RB RB RB RB RB A+ RB

S RB L RB S RB S A' +

RB

2.0

2.8

2.0

2.2 2.6 1.4

1.4

8.1 2.3 2.0 2.3

3.9 2.0 2.5 5.4 9.7

4.2

1.1 1.7

3.7

2.2

2.0

8.4 3.3 3.4 3.2 4.3

1.5

2.5 2.8 4.8

2.6

0.9 1.3

0.9

1.0 1.3 0.5

0.7

2.8 1.1 0.9 1.1

1.8 1.0 1.2 2.7 4.8

2.0

0.5 1.1

1.8

1.0

1.0

3.3 1.5 1.6 1.4 1.9

0.7

0.6 1.4 2.1

1.2

1.0 0.5

0.4

0.2-0.5 1.9 1.0

0.9

2.2 0.3 1.3 1.7

2.7 1.1 2.0 2.7 2.1

2.9

0.4

1.0

2.6

1.3

1.2

5.0 0.6 1.0 1.8 1.5

0.1-0.3

0.4 0.3-0.5

0.8

0.1-0.4

1 slab trig, by 2 skiers 2 slabs trig, by skiers, slab by snow ploughing slope fractured without aval. when 2 man stepped at one spot, 1 slab

by skiers 4 slabs trig 1 slab trig.

1 slab tris;

by explosives by 10-15 skiers

(NNW-slope) 2100 m

by skiers (N-slope, 2600 m) (NNW-slope, 2100 m)

1 slab trig, by climber

(NE-slope) 3 slabs trig, by skiers

(N-slope)

1 slab trig, by skiers

(N-slope) (S-slope)


2 slabs trig, by skiers

2 nat. slabs + 1 slab trig. by 2 skiers

slope fractured without aval. 4 man stepping at one spot 1 slab trig, by 9 skiers in a row (lower part)

1 slab trig, by 9 skiers in a row (upper part)

5 nat. slabs, 5 slabs

by explosions, 1 by skiers 1 slab trig, by skiers

2 slabs trig, by explosives 2 nat. slabs

1 slab trig, by Ratrac +

1 slab by explosives


2/3.02.

2/3.02.

10/11.02.

12.02. 14.02. 18.02. 25.02, 4.03.

5.03. 9/10.03,

86

86

86

86 86 86 86 86 86 86

25/26.03.86 26/27.03.86

27.03.86 2.04.86

2.04.86

L

L

M

L M S S M M M

L M

S L

L

A' + RB A' + RB A' + RB RB RB RB RB RB RB A' + RB

A' A+ RB

RB A' + RB

A'

5.7

2.0

1.9 2.8 3.3 2.7 9.1 7.0 3.9

5.7

7.1

2.5

5.2

3.1

2.8

2.7

1.0

0.9 1.4 1.6 1.2 3.9 3.4 1.9

2.6

4.5

1.3

2.5

1.5

1.4

0.3

1.4

0.4 1.5 1.3 1.1 1.5 1.3 1.3

1.5

1.6

1.5

1.8

0.4 -1.4

0.4-1.6

1 slab trig, by Ratrac



1 slab trig, by 3 skiers on a distance of 10 m 1 slab trig, by 1 skier

1 nat. slab + 1 slab trig. by a loose snow avalanche

1 slab trig, by 3 climbers or 1 falling skier same slab

212 Paul M. B. Fôhn

DISCUSSION

A. Roch Do you have an explanation why there is a difference in shear strength measured with a small shear frame compared with a larger frame?

P. Fôhn The larger the frame area the more likely it is that weak spots causing primary fractures are included in the sample. The larger the sample area the smaller the shear strength at least up to about 0.5 m (see also diagram "Correction factor vs. frame size area")

J. Dozier Your presentation does not distinguish between errors of "omission" and errors of "comission". In your cases where your evaluation was not successful, how often did you 1. predict avalanches (S or S' < 1.5) and they did not occur? 2. predict no avalanches (S or S' > 1.5) and they did occur?

P. Fôhn In the study, I did the success rating taking into account "omissions" and "comissions". In the presentation I could not comment for time reasons the "omissions" also. 1. If the surrounding slopes have been skied or bombed by explosions and there were no avalanches this was also rated as error. If we had no skiers (rather bad weather) and no explosive use this was rated as a success. 2. This was always rated as failure.

Ch. Stethem 1. Perla's work in Canada with different size shear frames was in homogeneous snow. In operations for testing weak layers we have found it difficult to place the larger frames. Can you comment on this? 2. In Canada we have found a more useful correlation between the stability index for new snow layers and avalanche activity than for old snow layers and avalanche activity. This appears to be opposite to your conclusion. Can you comment on this?

P. Fôhn 1. Shear frame measurements in seemingly homogeneous snow seemed us to be more difficult because there is no layer horizon to which a small or large frame may be aligned. In our slope measurements at or aside of real slabs the bed surface above which the frames had to be inserted were often marked by a different grain size or form or by small color differences. A large frame of area = 0.2 m is surely more difficult to align as a small frame of area = 0.05 m . 2. I did not analyze the data set in this respect, dividing cases with bed surfaces in new snow from the ones in older snow layers. Our data set contains not very many cases of new snow (snow 1-3 days old). So far I see no contradiction to your experiences.

G. Kappenberger There is a problem of measuring the shear stress close to the rupture zone of an already happened slab avalanche. I think that the rupture


event changes conditions, also of shear stress, in the critical slide layer, along the rupture zone of the slab. In the snowpack which did not move with the slab avalanche the shear stress has probably decreased. In this way the data set for avalanche situations may show to high stability indices giving an error source in the final results. How on that?

P. Fôhn It is most likely that the shear stress among other stresses in the snowpack sidewards of the rupture zone decreases after a slab release. If one would measure these reduced body stresses and introduce them in a formula for the stability index (e.g. S = r /r ), the resulting S would indeed be larger. The procedure is not this way. Only the shear strength r of this snowpack Is measured, the shear stress is calculated. In this way one stays on the safe side, because r is taken as unchanged. However the shear strength r , which will be measured, might slightly change ( r =f(r )), but this effect is included in the measurements of r .

s D.M. McClung In 1977 Perla published a paper in which he related shear stress at the weak layer (from avalanche fracture line profiles) to bed surface density and shear frame index. The result was that he got a better correlation with bed surface density. Have you been able to check these results with your fracture line profile data?

P. Fôhn No, because in our alpine snowpack the shear layers (lubricating layer, Gleitschicht) is often very thin (0.1 - 1 mm) we did not try to measure the density of this Gleitschicht nor the one of the bed surface. We have good data on the grainshape and grain size of the "Gleitschicht", bed surface layer and overlying layer as soon as the Gleitschicht thickness was > 0.5 mm. They will be published soon.

S. Ferguson 1. Although you say it is worthwhile for forecasters to have an index of stability, I must caution against using site-specific data to extrapolate for an entire snow field. For example, many very important weaknesses, like within surface hoar, may be quite isolated, since it depends upon micrometeorological conditions. On the other hand, weaknesses caused for instance by a slick refrozen rain surface are mesoscale phenomenon that are widespread. 2. Secondly, I object to your statement that "the Rutschblock" will find the weakest layer. It is true that many weaknesses will fail under stresses imposed by a jumping skier. However, there are some weaknesses, for instance thin layers of delicate, low density, new snow, which require a large stress distribution to fail, like an explosion in the air above the snow surface, or a blanket of rapidly deposited new snow. These layers do not respond to Rutschblock tests. Other types of location tests are required if your stability indices are to be applied to all slab avalanches.

P. Fôhn 1. Every data collection is to a certain extent site specific; if you

214 Paul M. B. F&in

want every point on earth Is specific. I agree, we have to find representative locations for measurements but this is a demand in every field of science. I disagree that surface hoar is quite isolated - at least in our climate; after some days of surface hoar development the shady slopes are all covered by a layer of surface hoar, I agree, sometimes thinner, sometimes thicker. 2. The "Rutschblock" will find with some exceptions the weakest layer with regard to a skier. Exceptions are: - the surface layer of 20-30 cm thickness may not be checked by the "Rutschblock", if it contains new or very loose snow except when it is covered by an ice crust. - if the instabilities are deeply covered by thick overlying layers of great strength, e.g. depth hoar buried by 1-2 m of stable snow, because the artificially induced stresses decrease with depth.

the stability index and various triggering...

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