To combat avalanches effectively a detailed knowledge of the properties of snow is essential. We must understand this subject and in particular why avalanches start on one slope and not on another. Furthermore we must know how avalanches travel, what speeds they can reach, and what effects of their forces can be predicted.
A first distinction to make is between snow which has retained its initial structure, that is a snow cover which has settled naturally, and snow the initial structure of which has been more or less completely destroyed by fractures.
Snow of the first kind we will call "natural snow" and that of the second kind "avalanche snow". This last term will also include the fine mixture of tiny particles-of snow and air in the form of an aerosol.
1.1 Natural snow behaves like a viscous and compressible liquid. Unlike solids,snow undergoes changes in form (shear deformation and stretching), and in volume, even under the lightest of loads. One of the most important problems in snow mechanics is finding as :general a relation as possible between the stresses and the speed of deformation. The simplest correlation of these two factors is expressed by the uniaxial tension of liquid according to Newton:
where:
The stresses are thus not proprotional to the speed but rather to the changes along axis x
The greatest forces in the snow cover are thus found in areas where speeds vary the most. Furthermore, experiments have shown that this relation does not hold except when the forces and deformations are of a very small magnitude. The size of a increases with the increase of the forces, and it is equally dependent on the force a exerted; in the case of compression the value of a is greater than it is under traction. Despite this, the relation is perfectly adequate for our purposes. The relation is equally valid for shear deformation perpendicular to axis x when the ordinary deformation forces are replaced by the forces of shear deformation.
Such relations as these are naturally no longer valid when the forces are of unlimited size since the strength of the material has finite limits.
Just as with the viscosity, the breaking strain is dependent on several factors and thus varies between quite large extremes. As a general rule the strength increases with an increasing specific gravity of snow. Furthermore the resistance to compression of a snow sample is approximately double its resistance to shear or tension (for the latter two are approximately equal). Finally the strength decreases as the force is applied more quickly, thus the smallest values for the resistance are obtained under shock.
Snow which has settled naturally manifests a marked stratification; consequently each stratum has a different strength.
The movement of an avalanche which slides - i.e. when the snow flows along the ground and when the snow particles remain in contact with each other - is above all affected by the forces of friction between the ground or the stationary snow strata, and the moving snow. For a snow velocity v the friction W over a given distance of turbulent movement can be evaluated in the following manner:
The first term is, in classical theory, considered independent of the velocity and proportional to the normal force N exerted perpendicular to the surface under load. The factor µ is the coefficient of friction.
The second term increases with the square of the velocity (v˛); it is also dependent on the specific gravity ( y ) of the snow in motion; on the coefficient of roughness K˛ (often designated § ) and finally on u the perimeter of the cross-section measured in the area where snow and ground are in contact.
A direct measurement of the above factors is seldom possible; for this reason their calculation has been carried out in part indirectly on the basis of observed avalanches.
Today values from 0.15 to 0.5 are usually used for the coefficient of friction; 400-600 ms for the coefficient of roughness which is determined by the snow type and the roughness of the underlying earth. The specific gravity of a flowing avalanche probably reaches 300 kp m3
With airborne powder avalanches - a movement analogous to that of an aerosol through air - the part of' the equation which is independent of velocity can be ignored, but instead the resistance at the front of the avalanche becomes very important. Avalanche snow in the form of an aerosol is of extremely low density with averages between 2 and 30 kp m3
These figures are based on the guidelines of the Swiss Federal Institute for Snow and Avalanche Research (SFISAR).
The height of snow (H) is measured vertically and is an indication of snow height at a given point. If the snow falls occurred during calm weather and are uniformly distributed, the vertical height of snow is independent of the gradient of the slope.
Maximum height of snow H max : maximum height of snow during a winter at a given place (for example at the emplacement of a structure).
The mean of the maximum heights of snow H max : the average over a given area (e.g. over an area to be controlled) of the maximum heights of snow H max calculated or measured over the period of maximum snow cover during one winter.
Extreme height of snow: H ext the greatest height of snow likely to be encountered, extrapolated for a defined place over a long period of time. On this matter only observations which have been carried out over many years will give reliable values. Thus when the observations have been carried out over many years will give reliable values. Thus when the observation have been made over a period go less than 30 years values for H ext will not, in general, be included.
Average of the extreme heights of snow H ext this is used for an area of terrain (e.g. in an area to be controlled) when the snow is extreme, more or less once every 30 years.
The thickness of snow D is measured perpendicular to the ground; the same categories as those for height of snow can be defined, thus Dmax, Dext, etc. The following relation exists between the height of snow and its thickness expressed by:
where:
The extreme heights of snow H ext in an area are determinant for drawing up an avalanche control projects The efficacy of avalanche defence works will depend above all on the reliability of this determination. Since observations of snow heights over a large number of years are normally not available for the area concerned, use will necessarily be made of the readings from nearby observation stations (e.g. the network of measuring stations of the institute at Weissfluhjoch). These readings, even if they are given in the form of water precipitation, will be representative of a large proportion of the territory. In other words the readings are not invalidated by local geographical features (e.g. by their position on flat land at the bottom of a valley). Consequently the values obtained in one place in fact give a picture for a wider area. Figures 1 and 2 show the average extreme snow heights in the Swiss Alps recorded at two altitudes and on the basis of observations over a period of 30 to 60 years. The calculation of the extreme snow heights at the emplacement of a structure is carried out in the following manner:
- Observation, if possible over a number of years, of the -maximum heights of snow Hmax on the site of the structure (with the help of graduated poles or by sounding). The local distribution of snow has to be measured, thus the frequency of measurements will depend on the features of the ground, in such a way as to measure local variations in snow height (such as in small gulleys). One can usually reckon on a density of 25-100 soundings or measuring poles per hectare. Furthermore, extremely valuable observations on the distribution of snow can be made during the spring snow melt.
- During the period of maximum snow cover in the area concerned, parallel measurements are taken nearby in an area which is as representative as possible of a large proportion of the territory. This allows us to obtain the averages of the maximum snow height
- Hmax. 'These measurements can be completed by including those obtained from well placed graduated poles. On this matter it should be pointed out that the area to be controlled does not normally lend itself to such measurements since it is an entirely special case (e.g. exposed to the wind or in its lee).
- The average extreme heights of snow H ext for Switzerland are determined with the help of Figures 1 and 2, or with other valid data (representative of a large proportion of the territory). Figures 1 and 2 can be used for altitudes of 1 600 m. and 2 000 m. For other altitudes it is necessary to interpolate or extrapolate linearly this data (see example). When the lines of the extreme heights of snow are close together great caution must be exercised. SFISAR is available for further information on this matter.
- To calculate the extreme heights of snow H ext at the site of a structure we start from the assumption that the distribution of snow will be similar from year to year regardless of the quantity of snow fallen:
If the measurements are taken over several years - which is, of course, desirable - H ext varies from year to year. In this case the greatest value of H max will be retained as valid. When the maximum snow heights for various years are almost identical the largest value of H ext will be chosen for the dimensions of the defences.
Example: The following values were obtained from measurements taken with graduated poles during three consecutive winters on the site of future defences in Dorfberg above Davos (alt. 2 266 m.):
Date: 8.2.1961 7.4.1962 17.1.1963
Hmax : 1.50 m. 2.20 m. 1.20 m.
Not far from there at the SFISAR measuring station at an altitude of 2 540 m. the following average values were obtained (valid over a larger proportion of the territory):
Hmax : 2.38 m. 2.75 m. 1.40 m.
Figure 1 allows us to read off the average extreme height of snow for the Weissfluhjoch area, thus H ext 2.50 m, valid for an altitude of 1 600 m. Figure 2 shows a value of H ext 3.00 m, for an altitude of 2 000 m. Thus the increase of H ext is of 0.125 m. per 100 m. rise in altitude. This yields a figure
H ext : 3.00 m. + 5.40 . 0.125 = 3.70 m.
The extreme height of snow on the site of future defences is calculated from the results of the three winters:
A value of 3.00 m. will finally be chosen, for effectively the highest value (3. 20 m. ) is less reliable since it is derived from a s smaller Hmax*
Circumstances leading to the release of avalanches:
a) Sliding slabs of snow
The snow cover of a slope is subjected throughout its thickness to creep, and, depending on the conditions of adhesion, it may glide along the ground (see Fig 3).
These movements depend on:
- the gradient of the slope,
- the thickness of the snow,
- the roughness of the ground, and
- the constitution of the snow (predisposition to deformation, friction, particularly when the stratum in contact with the ground becomes wet).
When these factors are not subject to local variation the velocity profiles are identical at all points. The weight of the snow cover is transmitted to the ground directly as normal pressure and as shear stress. This is the state of the neutral zone, characterized by the absence of local variation of forces of traction and compression parallel to the slope. Local variation of these factors produces areas of tension due to increased traction, compression and shear in the planes perpendicular to the slope. Slabs of snow break away when these particular local forces exceed the strength of that particular snow type.
A series of external factors enter into consideration here - such as an increase in the weight of the snow (e.g. a snowfall or a skier), or a decrease in the braking strength (e.g. an increase in temperature, snow crystal metamorphosis).
The initial break away of an avalanche usually results from a primary shear fracture. That is to say, a layer of snow parallel to the ground (either directly in contact with it or inside the snow cover) is subjected to too great a shear force so that tensile fractures higher up the slope and lateral shear fractures ensue naturally.
The other possibility is of a primary fracture due to tension (a primary fracture due to compression is unlikely, for the resistance of snow to compression is greater than its resistance to traction) which occurs when a section of snow perpendicular to the ground in the tension area can no longer withstand the forces on it. Shear fractures are immediately provoked.
b) Loose snow avalanches
These avalanches break off at one point, in snow which has very little cohesion, when a small amount of snow moves spontaneously or as a result of a minimal shock: stone fall or snow fall. The movement is propagated downhill in a restricted area and is amplified due to the increase in the mass of snow taken with it (pearshaped track).
c) Declivity and the release of avalanches
The entlest slope where avalanche release has been observed was a mere 17° gen percent) but such cases are generally inconsequential. Avalanche release is rare on slopes of less than 30° (58 percent).
On ground with a gradient of over 45° loose snow avalanches generally unload the slopes progressively during snowfalls, thus preventing the formation of stresses within the snow cover and also of slabs.
The destructive effect of avalanches is the result of their kinetic energy. If we exclude their shock effect which is of extremely short duration, the kinetic energy present is essentially dependent on the specific gravity of the snow and of the square of the speed of the avalanche.
Another important consideration in this respect is if, and in what circumstances, an avalanche could reach a site, which leads us to the question of deposit zones. The site of the deposit zone, where all the kinetic energy of the avalanche is absorbed, depends above all on the square of the speed and on the coefficient of friction and not so much on the total mass of snow in movement.
The velocity is in fact the most important factor when we are judging the possible effects of an avalanche. This is > , on the one hand, a function of the characteristics of the materials equation (page 4), and, on the other, of the local topography, rather than of the snow itself. When a stratum of snow fractures it is accelerated by its own weight. At the same time, and by virtue of the equation (or. page 4), the forces of friction increase. The acceleration increases until the driving force equals that of braking; from this moment on the speed cannot increase.
The period of acceleration is relatively short when we are dealing with snow slabs: when the distance travelled is approximately 40 times the initial height of the layer of snow in motion, 90 percent of its terminal velocity will have been reached.
With loose snow avalanches the period of acceleration is of longer duration; in fact at the beginning, the height of snow in motion and the motor force are minimal and increase gradually.
Generally we can say that the final velocity increases with the gradient and also with the thickness of the snow in motion.
In some cases the size of the break-away zone can also influence the speed. However, and this must be repeated - when the mountainside is regular and open, with no gulleys producing a canalization, the size of the break-off area has no effect on the speed.
In Figure 4 a) if the area above b-b avalanches, the speed of the avalanche across section b-b (terminal velocity) remains the same as if only the area above a-a had avalanched.
On the other hand, if the avalanche is canalized the shape of the break-off area is significant. Figures 4 b) and 4 c) show a schematic representation of two different cases. The decisive value for the speed is the quantity of snow Qm which passes through section a-a per unit of time.
This can be estimated by use of the equation:
where:
Thus:
where:
If we assume exactly the same conditions of gradient of slope and thickness of avalanche snow for the two cases illustrated in Figures 4 b) and 4 c), we immediately see in the case of 4 c) that there will be a greater discharge of snow; and with the height of snow flow being equal a larger Qm and a greater speed through section b-b results. In the same
figure we see that if only the right-hand portion of the slope avalanches, the volume of snow will be halved with a corresponding reduction in speed.
These brief considerations are of considerable importance when drawing up maps of danger areas and in the planning of avalanche defences. Equally they provide certain criteria for appraising the protection they can offer.
Different shapes of starting, transit and arrest zones.
