H. R. in der GANO and M. ZUPANCIC Federal Institute for snow and Avalanche Research
Weissfluhjoch/Davos
The slow, downhill gliding of the entire snow cover along the ground leads on uneven slopes to the formation of cracks and slulfs. While the cracks form as a result of the gliding, such a relationship for the slulf release is not clear. As a result of field investigations over several years, the influence of ground surface roughness, terrain shape and snow characteristics has been determined. The snow cover always glides on a wet snow boundary layer several millimeters thick and in all cases reaches a steady glide velocity. A method for measuring the glide velocity is described. A glide velocity equation is derived for these relations, assuming a free-gliding snow block and a simplified friction model.
Field observation of the spatial and temporal coincidence of slulfs running on the ground with rapid glide motion lead to the inference that snow gliding participates in the release of the slulfs.
RESUME
Le glissement lent de toute la couverture de neige sur le sol est accompagne dans des pentes irregulieres de la formation de fissures et de devalements. Bien que Jes fissures soient causees par le glissement, la relation de celui-ci avec les devalements n'est pas claire. En se fondant sur Jes resultats d'observations faites dans le terrain pendant plusieurs annees, on a determine l'influence de la rugosite de la surface et de la forme du terrain ainsi que des proprietes de la neige. La couverture de neige glisse toujours sur une couche de neige mouillee epaisse de plusieurs mm et elle atteint dans tous Jes cas une vitesse de glissement constante. On donne une methode de mesure de cette vitesse. Dans ces conditions et en supposant un bloc de neige glissant librement, on derive une equation pour la vitesse du glissement avec une hypothese simple pour le frottement.
La coincidence spatiale et temporelle, observee dans le terrain, des devalements et du glissement rapide permet de supposer une relation entre ces deur phenomenes.
I. INTRODUCTION
The down-slope gliding movement of the snow cover on the ground has long been known to the inhabitants of the middle-European mountains. In special circumstances the generally invisible gliding leads to the formation of cracks and folds in the snow cover. In critical situations an accompanying phenomenon is the fracturing of the snow cover to the ground, whose result may vary from the fall of small sluffs to an extensive avalanche according to snow conditions and shape of the terrain (fig.
1 and 2.) The effects of vigorous glide motion often appear locally as heavy damage:
- Destruction of the surface soil layers by plowing action;
- Injury to the vegetation cover, damage to young plants and older tree groups;
Displacement of natural and artificial obstacles such as boulders, clumps of trees, hay huts, stone walls, avalanche defenses, fences, stakes and paths.
2. DEFINITIONS AND STATEMENT OF THE PROBLEM
Gliding of the snow cover on a slope is a slow, downhill motion in the direction of the fall line which results in displacemellf of the entire snow cover.
Fig. I- Formation of glide cracks and gliding snow sluffs in the snow cover, area
"St. Antonien ", Canton Orison, altitude 2000-2200 m, SSE-slope, vegetation grass.
This process of motion is to be clearly distinguished from internal s11ow creep, which is the resultant of settlement and internal shear deformation parallel to the slope.
The cause of both of these motions is the internal weight of the snow cover which generates forces both parallel and perpendicular to the slope (fig. 3).
Under natural conditions the maximum velocities of these motions reach the following orders of magnitude:
Creep Gliding
mm to cm per day mm to cm per day and in comparison Avalanches m per second HAEFEL1(1) proved with snow blocks on glass that:
- For given conditions of the snow-glass interface the gliding velocity increased linearly with shear stress and reached in each case a constant value;
- The gliding velocity depends on the stress condition and on the interface tem-perature;
- The friction coefficient decreases to a low value with the change from dry to wet gliding.
HAEFELI also suggests that the gradual change of the very slow gliding velocity to the dynamic motion process and thus avalanche formation results when a critical gliding velocity is exceeded. According to BucHER(2) the glide velocity, in analogy to creep velocity, is determined by shear stress and snow viscosity. High velocities can thus occur when relatively high temperatures reduce the value of the highly variable viscosity, i.e., in the basal layer of the snow cover when groundtemperatures are above freezing. Contrary to HAEFELI, BucHER ascribes the formation of gliding snow sluffs, at least during snowfalls, not to glide motion, but to the formation of shear fractures in the lowest boundary layer as the shear strength decreases.
60
Hg. 2-Formation of folds in the pressure zone of a gliding snow cover.
The investigations to date leave unanswered the question of the relationship between snow gliding and formation of gliding snow sluffs. The glide cracks, however, are clearly a result of rapid gliding.
3. RESULTS OF THE FJELD INVESTIGATIONS
During several years of field investigations and measurements we have attempted to understand the phenomenon of snow gliding under natural conditions. The results
shear deformat on
settlement
~
total displacement~
~
_,. _,.---
--Fig. 3- Schematic diagram or the creep and glide movement or the snow cover.
are summarized here and illustrated with the example or the winter 1962/63. Infor-mation about the research sites and the arrangement of the measuring locations are given in figure 4. The measuring methods are brierly described in Section 3.3.
3.1. Character of the Gliding Motion
- The generally uneven course or the motion consists or periods or both uneven and steady gliding interrupted by periods or repose;
- Continuous motion can be followed by jerky motion;
- The velocity reaches a maximum constant value on all of the slope zones (pressure, neutral and tension), on smooth as well as rough ground, and arter crack formation.
3.2. External lllf/11ences
3.2.1. Roughness of the Ground
The primary condition for the gliding movement is a relatively smooth ground surface.
Two influences must be distinguished:
62
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6,;
L5o0
H
,soo'°" """'
JIO 3500
lD :mJ
250 2500
~ mt,UlJl'lnljli.oat,ons(!)-@
a!IIIU!Se 2DSO· 2Cl'i'Om, SSE·sl.DPe. &f9e ol l'ICI :16·13°, ...egetalai 9"i15511wllf ~
meau-n;i toc11,on(i; belwttn ~ t i n g Sll'lJtt,..ru .allil~ l'l30m.S5E, )6•, !i,HS•dwilrf 5h'ub5
'111'11! sro.vc011er Sm abo.-e measur,ng l~ t
- - ~ - J - - - t - - - - : ; , - ----1- - + . : t - " - - - t
A£S!l!ZdVIO)N"'9ffl!IN'll
t'Pf:t'ffl:fll.111. are• "OPS", me.u,.,.ir,g loc ■cns I '6
~ ~ . a l vu "Sopptm\lhcl", ~•SUT9 locat,on 1
""""'
!iO 1(1)
lD
Mlr - - - - -1 - -- - - ...
--lyl'----+----+ ---~---r
·~ ~
•c ,a s 0
.,.
-s·IS
·lO
60 ,o
QO"C
"':-~__;;;,~~i=='il---1.W.
Fig. 4-Movement of the whole snow cover over the ground for two areas in the
"Dorfberg" near Davos, winter 1962/63 (compared with air temperature, snow
I. Simple friction between snow cover and the ground ;
2. Interdigitation between snow cover and ground, such as that introduced by vege-tation.
Experimental investigations with snow on a natural surface are not available.
As a result of field measurements the friction coefficient for snow with a wet underlayer lying on grass can be roughly estimated to have the order of magnitude of 0.2 ... 0.3.
Several poorly-defined effects are hidden within the overall concept of the inter-digitation between snow and ground. In nature many examples are found varying influence on each other after a certain length of time.
Figure 4 shows the glide paths and velocities at six measurements sites arranged as a result a few days later motion ceased until the end of the winter. In the lower sites (2 and 3) it persisted for two to three weeks. The strain rate in extension of the snow cover for the entire winter was: accompanied the continuous gliding in this compression zone.
Slopes of gentle gradient within steep terrain hinder the glide process through the introduction of zones of compressive and tensile stresses. The snow cover reacts to middle-European climate the ground surface temperature under normal snowfall conditions is at the freezing point on south exposures up to an altitude of 2400 m.
The melting process in the bottom layer leads to ablation of observable quantities of snow:
64
- SSE slope of 40°, altitude 1800 m, from end of November 1962 to mid-March 1963, the ablation was 17 mm of water, or approximately 20 cm of snow;
- SSE slope of 30", altitude 2050 m, 19 November 1964 to 16 March 1965, the ablation was 73 mm of water, of which 12 mm melted in the first 14 days.
In addition, the formation of the wet snow layer at the bottom of the snow cover may be caused by:
Rainfall prior the first snow deposition;
Melting by transmitted solar radiation for snow covers less than 30 cm thick;
Intrusion of liquid water flowing along the ground.
Snow cover accumulation
Each increase in snow cover thickness and the corresponding increase in weight on an inclined plane leads to an increase of the shear stress and of the gliding velocity.
In figure 4 this dependency of glide velocity on snow weight is clearly shown during the deep snowfalls during the latter two-thirds of December. This influence cannot always be so clearly perceived, because it is obscured by changes in characteristic properties of the snow cover. It is important to emphasize that each effective increase in weight gives a higher but still constant velocity. In the given example in figure 4 the velocity increase to the new value during and after the snowfalls is strongly delayed for measuring Sites No. 3-7, in contrast to Site No. 2. This resulted from the widely different snow conditions for the bottom layer, for Sites 3-7 were buried under a lightly-consolidated snow layer about 20 days old, while No. 2 was still uncovered prior to the deep snowfalls. This example shows how sensitive the gliding process is to characteristics of the snow cover and especially to those of the bottom layers.
Temperature and Viscosity
The plastic deformability of the continuous natural snow cover exerts a direct influence on the gliding process. Because the snow viscosity is so strongly depended on temperature, each temperature change must cause a pronounced change in gliding velocity. This is effectively shown in figure 4. Around the middle of January the gliding velocity strongly decreased at all measuring sites when the mean snow tem-perature fell 3.3 •, and finally with persistent low temtem-perature stopped completely.
On the other hand, after a longer quiescent period, the gliding process was strongly renewed in the middle of February when the mean cover temperature rapidly rose 3 •.
With further temperature increases it once more achieved a velocity maximum, which was lower than that of the initial motion period because in the meantime the snow
[Z]
Fig. 5- Experimental arrangement for measuring the gliding of the snow cover.
4. MECHANISM OF THE GLIDING MOTION
Definitions:
glide velocity v11 [m sec -11
d [ml y [kg m-31
1:,a [kg m-2]
snow cover thickness perpendicular to the slope density of the snow cover
stresses due to the snow block, respectively parallel and perpendicular to the slope
R [kg m-2] total friction resistance µ coefficient of sliding friction
t5 [ml thickness of the viscous boundary layer 7/ [kg sec m-2] coefficient of viscosity of the boundary layer.
From the glide experiments of HAEFELI and from the results of the field measure-ments it can be assumed that a free-gliding snow block on an inclined plane reaches a definite sliding velocity determined by the weight of the block and the total friction.
The stresses working on the block must therefore be in equilibrium:
1: - R
=
0 J-,;=
d. y. sin 1/J (I)For a snow block resting on a wet snow boundary layer, the existence of a lower limiting value of slope angle for glide motion and of a constant glide velocity leads to the simplified model in figure 7. There are two components of friction, dry (R1) and viscous (R2),
such that R = R1
+
R2 (2)and R1 is proportional to a
R1
=
(1. µ J C1=
d. y. cos tp (3)66
Fig. 6 (a and b)- lnstallation of the potentiometer box and the gliding shoe on a measuring location.
The viscous component is associated with a boundary layer of thickness
o
and viscosity 17:(4)
snow block
Rt (dry! Rz lviscOl/s)
Vu•
f
·d·T(sin'i-p-cos'J-1Fig. 7- Snow gliding and friction model.
Combining equations (I), (2), (3), and (4) yields the equation for glide velocity:
0
Vu - - • d • y (sin 1/J - µ cos tp)
1J (5)
The glide velocity increases in proportion to the weight of the snow block and the slope angle (almost linear over the range 20-50 °), and decreases with increasing dry friction. In addition it depends on the relationship of boundary layer thickness and viscosity. This equation must be applied with caution to natural conditions due to its greatly simplified character. In figure 8 the glide velocities as a function of slope angle observed in the field are compared with values calculated from equation (5).
Because the measured values are largely mean velocities and the velocity equation is valid only for a free-gliding snow block, the viscosity and friction coefficients (1J, µ) for given values of
y,
d ando
must be relatively large.This is also shown by figure 8. Moreover, a few values of maximum glide velocity have been measured after crack formation which approach those for free gliding 68
°'
IO,s -I
'°
JS I
JO
I
25--I
20
15
~
1 / /fl I I
0
I
I
...
/ I 7
.
I / II
____ Or/
I I I I
;
---- Do /
I
0
O
0 0
✓ /
0 0 ~ ~
I
DO / J--,/ I
0 0
0 0 0
vi
I, ~
< \ ~
,.,,.,.,.
/-- --- j
10 so 10~ 500 1000
Fig. 8-Glide velocity as a function of the slope plotted for the equation Vu
= -
t5 d· y (sin 1J}-µ. cos 1J1)I
y·d 200 kg m-t5 0,8 • 10-2 m 2'1/ Vu m sec-1
where 7/
=
coefficient of viscosity for the boundary layer [kg sec m-2]µ = coefficient of glide friction Measured values in the field:
o mean velocity on grass over several days }
□ mean velocity on rough ground continuous snow cover
• momentary maximal velocity on grass
5000 10000 20000
velocity Vu ITVTl per day
(see figure 4, Site 7). These values yield a viscosity coefficient of the boundary layer of 104 to 105 when c5
=
0.8 cm (observed) and I ' ~ 0.3 for grass (in agreement with field measurements). Such values of the viscosity coefficient for wet snow are reasonable ones.5. GLIDE CRACKS AND GLIDING SNOW SLUFFS
Glide cracks are half-moon to sickle-shaped crevices which open in the snow cover as a result of tensile failures during rapid gliding. They occur most frequently in the tension zone of terrain breaks and extend through the snow cover to the ground.
According to snow conditions and shape of the terrain they may reach widths of a few meters to several tens of meters.
Gliding snow sluffs are small avalanches which slide on the ground and likewise occur at times of rapid snow cover gliding. Most of them break loose all at once as a snow slab, but it is also possible for sluffing of the snow first to occur long after cracks have formed.
Fig. 9- Formation of glide cracks and gliding snow slulfs in the area of" Dorfberg", near Davos, situation of April 30, 1965.
According to results of the field investigations, snow gliding which follows tension crack formation also leads to non-accelerated motion. ln this case the change-over from a slow gliding to the dynamic motion process does not take place. This deter-mination is especially important for answering the key question: Is gliding the direct cause of gliding sluff formation, is it only a secondary factor, or does it play no part at all? While for glide cracks the causal relationship between gliding and crack formation is obvious, and has also been confirmed by field measurements of glide velocities in the tension and neutral zones, a satisfactory explanation is presently lacking for the release of sluffs.
70
If the field observations are taken into consideration and sluff and crack formation equated with various snow glide situations, then the following analogies can be estab-lished between sluffs and cracks on one hand and between both phenomenon and snow gliding on the other.
5. I. The local occurrence of sluffs closely coincides with that of cracks and rapid gliding. For example, sluffs and cracks both occur frequently on smooth slopes covered with long grass where the angle exceeds 34°, can occur on rougher ground only on slopes over 40°, and do not occur at all on slopes less than 30°. In both cases the fracture sites are located directly at convex terrain breaks. The south-facing slopes below 2000 m-i.e., the climatically-determined snow gliding zone- are also the principal localities for sluff and crack formation.
5.2. An analogy also exists in the times of occurrence. Over a long period of observation (I 955/56-1964/65), the incidence of both sluffs and crack formation is, surprisingly enough, about equally divided among the months from October through April.
5.3. These appears to be little difference between the influence of the weather factors temperature and precipitation. Increases of snow cover thickness and temperature rise each contribute to formation of sluffs and cracks about half the time.
There thus exists clearly-indicated parallels between the glide process of the snow cover and occurrence of gliding snow sluffs, which lead to the inference that snow gliding is in some manner involved in release of the sluffs.
Another problem thus is added to those already existing in avalanche research.
( 3) EUGSTER, E., Schneestudien im Oberwallis und ihre Anwendung auf den
Lawinen-verbau, Beitriige zur Geo/ogie der Schweiz, Geotec/111. Serie, Hydro/ogie, Lieferung 2, 1938.
( 4) GEIGER, R., Das Klima der bodennahen Luftschicht,,, Die Wissenschaft ", Bd. 78,
1961.
( 6) HAEFELI, R., Schnee, Lawinen, Firn und Gletscher lngenieur-geologie von L.
Bendel, II. Hlilfte, Wien 1948.
( 6) HEss, E., Erfahrungen tiber Lawinenverbauungen, Nr. 4 der Veroffentlichung
des Eidg. Departementes des Innern tiber Lawinenverbauungen, Bern 1936.
(7) in der GANO, H., Beitrag zum Problem des Gleitens der Schneedecke auf dem Untergrund, Winterbericht des Eidg. Institlltes fiir Schnee- 1111d Lawi11e11forsc/11111g, Nr. 17, 1954.
( 8 ) in der GANO, H., Ergebnisse der Gleitmessung, Winterbericht des Eidg. lnstilutes
fur Schnee- u11d Lawi11e11forsch1111g, Nr. 20, 1957.
( 9) in der GANO, H., Ergebnisse der Gleitmessung, Winterbericht des Eidg. /11stit11tes
fur Schnee- und Lawi11e11forsc/11111g, Nr. 22, 1959.
( 10) in der GANO, H., Schnee-und Lawinenforschung im Dienste des Gebirgswaldes,
Mitt. des Eidg. Institutes fur Schnee-1111d Lawi11e11/orsc/11111g, Nr. 14, 1959.
( 11) MATHEWS,
w.
H., and MACKAY, J. R., Snowcreep Studies, Mount Seymour,B. C.: Preliminary Field Investigations, Reprint from Geographical Bulletin, No. 20, 1963.
( 12) ZINGG, Th., Wasserwert und Abbau der Schneedecke, Verhandlg. der SNG,
Davos 1950.