Inhabitants of Alpine valleys have always tried to build their houses or mountain pasture chalets in safe places. When this was impossible they tried to deviate the avalanche with artificial obstacles copied from nature. For example, they built houses with flat roofs incorporated into the hillside, or they built a spur in the shape of a wedge behind a building if there was no shelter from a large rock nearby. In eighteenth century Switzerland ditches or mounds were built. Certain churches were constructed with a splitting wedge integrated into their up-slope wall.
To protect routes of communication, sheds were built from either wood or stone such as can still be seen on the south side of the Splugen. For Switzerland, Coaz mentions structures at 1 603 m. in his work of 1881; these were probably built at the beginning of the nineteenth century.
With the exception of Loéche-les-Bains in Valais,we have little or no information on the dates of construction. This hot springs resort, where archaeological remains from the Téne period have been found, has always been much frequented since that period. The municipal archives contain documents allowing us to discover the history of avalanches in the area from 1518 onwards.
The first deviating dams are mentioned in 1569. A few years later, the proprietor of the "Maison Blanche" inn built a wall-dam 80 m. long, 2.3 to 4 m. high and 80 cm. thick at its coping, backed with earth-fill to threequarters of its height. This wall, built around 1600, is still in a relatively good state of repair. Similar structures were built in 1721 with the same system of earth-fill, but with 2 m. of earth behind the coping and a batter of two-thirds. In 1829 this structure was completed by even larger works.
The Weissfluhjoch guidelines define in Articles 5b) and 5c) the various structures for deviating, braking or preventing (or intercepting) avalanches.
"Structures with dimensions in proportion to the kinetic energies of avalanches such as dams, walls, galleries, deflecting walls, and sheds, can deviate, divide or channel a moving avalanche." (Article 5b) of the Weissfluhjoch guidelines)
When dealing with the safety of communication routes defences which deviate avalanches are still widely used. They are generally more economical and more reliable from the word go than defences designed to anchor the snow to the slope in the starting zone.
The least expensive and most effective method must be found for each particular case.
When the starting zone is a large catchment above the forest limit and the road crosses a narrow gulley in the danger area, sheds without doubt offer the best protection. A shed protects the road during winter, but in summer too it ensures its safety from landslides and stone fall. The sheds constitute the only completely reliable protection during winter too. (Fixing the snow to the slope by means of rakes or bridges could always leave a passage open for small avalanches which would nevertheless disrupt traffic) .
One can also make do with building sheds only in the most dangerous gulleys and rely on closing the road during periods of exceptional avalanche risk. This would entail preventive closure of the road for two or three days each winter.
Dams or walls to channel avalanches are necessary when the shed is built at the outlet of a gulley on to an alluvial cone with a relatively low gradient. The dams must not converge in order to economize on the length of the shed,for there would undoubtedly be failures due to the accumulation of snow on the roof and overflows of snow at the sides, which would block the entrances to the shed.
Deviating dams are intended to change the direction of an avalanche or stop it from spreading out in a certain direction. Their efficacy depends not only on their height, but also on the gradient of the slope and the angle of deviation.
When the deposit zone is too flat, the dam blocks the avalanche, filling the area with snow, thus making it useless for subsequent avalanches. On the other hand, if it is built on a slope which is too steep the structure will have to be very high which might compromise its realization on the technical level.
Deviating dams or walls are most effective when they are used to raise the sides of a gulley thus increasing its height, and stopping the avalanche from leaving its channel. The effectiveness of walls or dams is also dependent on the angle of deviation which should not exceed 30 . The gentler the angle, the easier the deviation of the avalanche and the smaller the load on the structure.
Protection of isolated structures (buildings or pylons) is undertaken with spurs or wedges built against the building or in its immediate vicinity. These defence structures divide avalanches. The angle formed on the hill-ward side of the wedge should not be greater than 60° . Further more, the sides must be of sufficient length to prevent any eddying of the snow past the ends from engulfing the protected structure.
In order to construct spurs or wedges, the speed and height of flow of the avalanche
must be known. The required dimensions and the loads avalanches will impose on a wedge are
calculated in the same way as for deviating banks (see Pigs. 20 and 21).
The same principles of design for the construction of sheds also pertain to the construction of galleries which fulfill the same function.
"Obstacles built to withstand the kinetic energy of avalanches can be erected in their path in order to cut them off (dams) or to shorten their trajectory (wedges, spurs, or wedges in the form of pre-cast concrete tripods)." (Article 5c of the Weissfluhjoch guidelines)
Structures for braking avalanches were first conceived of in Austria. Their final aim is to split up an avalanche into several streams which then exhaust their energy against each other when they join up again. These obstacles are placed in a chequer-board pattern in the trajectory of the avalanche, which is thus spread out. As a result, the height and speed of the flow of the avalanche are reduced; in other words the force (which is proportional to the square of the speed) decreases.
The heavier the snow the better the result; therefore, these structures must be built at the lowest possible altitude.
Furthermore, in order for them to be effective these structures must be placed on a gentle slope of not more than 12 to 15 (i.e. corresponding to the minimum coefficient of friction of moving snow) and they must be sufficiently long and wide since the avalanche will be spread out by these obstacles.
Braking structures can be built with earth, with concrete, or with concrete and earth and can be protected with stones on the side facing up hill. Their size can also be calculated.
Usually, braking structures will have to be used in combination with a containing structure to block any part of the avalanche the movement of which has not been sufficiently slowed down.
When one is planning to use structures of these type, some must not delude oneself: these structures do not perform miracles and should only be used in the same area where a normal avalanche would have stopped of its own accord. These structures thus provide us with effective measures against avalanches of catastrophic proportions.
Results obtained so far can be regarded as satisfactory; nevertheless we must not forget the failures and the strengthening of inadequate old defences, as well as possible accidents. For this reason, since determination by calculation provides us with a greater control over the situation, analytical methods should be used for every case, even if it entails the estimation of one of the factors should this not be measurable. By following this procedure, many of the mortifying setbacks which could befall the planner will be avoided. Furthermore we must not forget that despite the considerable advances in our knowledge of the properties of snow, there will always remain certain unknown factors which may necessitate additional works.
The implementation of such a project relies on a knowledge of the type and magnitude of the forces which will be exerted on the structure in the most extreme possible case. The gallery does not constitute an obstacle, for the trajectory of the avalanche is hardly changed by it. The static and kinetic forces exerted on the roof of the gallery comprise the sum of the weight of the snow cover, the load exerted by the moving avalanche, and the force of deviation and of friction. The gallery must be designed to cope with these forces.
The Weissfluhjoch Institute in Switzerland placed several measuring devices on the roofs of old galleries. The measurements carried out since 1962 record the maximum pressure measured normally (Pn ) and parallel to the roof (Ps) which allow us to calculate the coefficient of friction ( µ ).(mu)
For these readings to be valid they must be taken over a series of years. Results so far, from readings taken between 1962 and 1972, are presented in the graph below. Note that the avalanches do not occur each year. Research is also carried out at Weissfluhjoch where a slide built next to the Institute gives more accurate and detailed results.
The results obtained are for avalanches flowing over a gallery. Airborne powder avalanches flow above the structure exerting negligible friction against it. When a gallery is very short there is a chance that such an avalanche may envelop the structure completely exerting a light suction on it (of the order of - p < 100 kg./m˛ from observations and calculations).
µ = Ps / Pn
Legend for Figure 18:
Normal pressure (Pn), parallel to the roof (Ps) and coefficients of friction µ calculated
µ = Ps / Pn
Legend for Figure 19:
Average value for µ based on 14 readings taken between the edge and the centre of a gallery: A maximum = 0.32 (at 1.5 m. from the centre). µ at the centre = 0.27
However when calculations are being made µ is taken as >= 0.40.
Example of the calculation of the forces exerted on a gallery:
An extreme case of avalanche is taken as the base for calculations.
The forces exerted by snow usually comprise:
a) the weight of snow accumulated on the roof of the gallery before and during the passage of the avalanche an in certain cases the pressure exerted by the creep of snow
Under average conditions the following values are used
ya = density of snow = 400 kg./mł
da = thickness of snow on the roof during the passage of the avalanche = 1.5 - 2.0 m.
Normal pressure: Pna = ya . d a .cos B (kg./m˛)
where B = gradient of the roof
b) the weight of snow flowing over the tunnel
An average value of yi = 300 kg./mł is used for the density of moving snow.
Height of flow = di
Normal pressure: Pni = yi .di . cos B (kg. /m˛)
c) force exerted on the roof of a gallery due to a change in the direction of flow of an avalanche by angle
Length of change of direction = L
Speed of avalanche = Vi
In practice the change in slope between roof and terrain must be placed as far above the gallery as possible.
d) the sum of normal pressures (P n ) exerted on a gallery is thus:
e) forces of friction
y = 0.4 is taken as the coefficient of friction and, with the preceding calculations we thus obtain:
- for stationary snow
- for the weight of avalanche snow
- for the change in direction
f) the sum of frictional forces exerted on the gallery during the passage of the avalanche (Ps ) is:
g) weight of avalanche deposit
ya' = 500 kg./mł is the value generally used; an average value of the height of deposit is calculated da' , yielding a normal pressure of:
h) additional soil pressure exerted on the up-side wall of the gallery due either to the avalanche's force of friction against the ground or to the extra weight of a deposit of snow;
i) static pressure of snow against the face of the gallery, should this be entirely covered by an avalanche;
j) forces exerted on the gallery caused by avalanches which come down opposite it, from the other side of the valley.
Naturally, all the forces listed will not be applied at the same time, and never to their maximum values.
Calculations of the speed of avalanches, the respective heights of their flow and of their deposits, as well as the length of their deposit zone should all be carried out by a specialist.
To begin with, we remember that in order to carry out these calculations a series of data must be at hand. We need firstly a detailed knowledge of the area in which the avalanche occurs, the lie of the land, its exposure and, of course, of the area of avalanche release.
This data cannot be obtained merely from a detailed topographical map; the area must be known at first hand so that all possible indices of the precise path of an avalanche can be gathered. This of course includes a critical appreciation of information from local inhabitants as well as all information gained from photographs, old chronicles, and records of a technical or meteorological nature (height of snow, prevailing winds, etc.).
Following this, one proceeds to make an approximate map of all the respective surfaces and slopes an avalanche will travel over from its release.
Starting from actual typical avalanches, the height of sliding snow will be determined (e.g. 50 em. in a normal case, 120 em. in an extraordinary case and > 120 em. for an avalanche of catastrophic proportions).
By analogy to the calculations used in hydrology, the height of the avalanche flow along the slope, according to its gradient and section. As well as the length of deposit at the bottom of a gulley, can be determined. These calculations must be carried out by an expert since some of the data are based on interpretation of local conditions.
In the case of canalization of the avalanche, the new height of flow can be determined so that the relative heights of the banks can be specified.
With regard to barriers (be they combined with braking structures or not) their minimum height can be determined with reference to the fact that the avalanche must be brought to a standstill by forcing it to climb until all its kinetic energy is exhausted.
In this case the vertical height corresponds to the vector of energy. In hydraulics, the latter is given by Bernoullil´s equation and is composed of the sum of heights representative of the kinetic and potential energy. For avalanche snow this formula needs to be adapted since forces of friction are generated during flow changes. Nevertheless a rough estimate can be obtained for the required height of the barrier (H D) by ignoring this influence, thus yielding the condition:
V = speed near obstacle
HL = height of flow of avalanche
HS = height of natural deposit of snow in front of the obstacle
It will be deduced from this formula that the arrest of an avalanche by a barrier
is only practically possible when the speed of the sliding mass of snow is reduced.
For this reason, this type of structure is normally used with devices for braking
the avalanche, and they are usually built in the bottom of the area where a
"normal" avalanche spreads out and stops
(this area is distinguished from the avalanche path by a gradient of 12-150 or less).
We now provide a few formulae for the use of specialists, but we must advise novices not to carry out the calculations themselves.
Formulae by Salm, Sommerhalder and Voellmy:
y = coefficient of friction (in general 0.15-0.3 and 0 when the snow is wet)
h1 = height of flow of avalanche (m.)
V = speed of avalanche (m./sec.)
ha = height of snow in deposit zone (m.)
s = length of deposit zone
so = distance required to reach maximum speed
F = area of the section (m˛)
D = distance measured in the direction of the avalanche flow between the bottom of the reverse slope and a point in the zone of deposit (such as a building)
U = width of the ground over which the avalanche travels
R = hydraulic radius
bm = average width of avalanche (m.)
Q = volume of snow/sec.
The calculations are based on the results of visits to the area, examination of documents available, studies of longitudinal sections of the avalanche slope the avalanche circumstances and the choice of the values for the different variables (specific gravity of snow, etc.).
The height of the flow of the avalanche is then determined from the longitudinal sections. Initially h1 is practically ho. As the slope changes h1 varies according to the formula:
In gulleys h is a function of the cross section of the gulley and of the quantity of snow flowing per second: (Q)
The height of snow flowing through a typical cross section is calculated by taking successive approximations for increasing heights until Q is identical to Qo.
When the gradient varies through the gulley the following formula is used:
and the calculation is carried out in the same manner.
Formula for speed through gulleys:
Formula for speed down slopes:
Maximum speed down slopes:
This last speed is reached when the avalanche has travelled approximately so = 25 h1
Formula for the speed of an airborne powder avalanche:
Average height hs in the deposit zone:
The length of the deposit zone is derived from:
The cost depends on the following three factors:
- access to the site determines the type of machinery used and the length of time required to complete the works, depending also on altitude;
- type of ground; depending on whether huge blocks of stone which need blasting or whether mere soil and broken stones are encountered, the cost of earthworks per m can double;
- the prices of civil engineering works in reinforced concrete for galleries, road bridges, etc. vary from area to area.