Environmental Engineering Reference
In-Depth Information
Range or country
N
α
R
s
Canada
126
0
.
93
β
0
.
86
0
.
74
β
+3
.
67
◦
Alaska
127
0
.
76
0
.
63
β
+4
.
68
◦
Colorado
52
0
.
70
0
.
67
β
+2
.
50
◦
Sierra Nevada
130
0
.
77
Haute Tarentaise
168
0
.
82
β
+2
.
82
◦
0
.
81
2
.
69
◦
Table 2.1.
Determination of α for different mountain ranges. N refers to the number of sites
for each regression analysis. Data collected from [ADJ 96, MCC 91]
113 avalanche paths in western Norway, these authors have found that
1
.
7
◦
.
α
=0
.
96
β −
[2.1]
The regression coefficient
R
is fairly good (
R
2
=0
.
93) and the standard deviation
s
is
relatively small (
s
=1
.
4
◦
). Table 2.1 summarizes the values of
α
for various mountain
ranges.
Many extensions of the early model developed by Lied and Bakkehøi have been
proposed over the last 20 years either to tune the model parameters to a given
mountainous region or adapt the computations to other standards. For instance,
subsequent work on statistical prediction of avalanche runout distance has accounted
for other topographic parameters such as the inclination of the starting zone or the
height difference between the starting and deposition zones. Although statistical
methods have been extensively used throughout the world over the last 20 years
and have given fairly reliable and objective results, many cases exist in which their
estimates are wrong. Such shortcomings can be explained (at least in part) by the fact
that for some avalanche paths, the dynamic behavior of avalanches cannot be merely
related or governed by topographic features [MEU 04a, MEU 04b].
2.2.2.
Fluid-mechanics approach (avalanche-dynamics models)
Snow avalanches usually take the appearance of viscous fluids flowing down a
slope and this observation has prompted the use of fluid-mechanics tools for describing
their motion. However, there are impediments to a full fluid-mechanics approach: a
wide range of particle sizes (often in the 10
−
3
to 1-m range), composition that may
change with time and/or position, ill-known boundary conditions (e.g. erodible basal
surface) and initial conditions, time-dependent flows with abrupt changes (e.g. surge
front and instabilities along the free surface), etc. Testing the rheometrical properties
of samples collected in the field remains difficult. To give examples of materials
involved in rapid mass movements, Figure 2.5 reports the different types of snow
observed in avalanche deposits. Because of particle size and thermodynamic alteration
(snow is highly sensitive to changes in air temperature), using classic rheometers with
these materials does not make sense. All these difficulties pose great challenges in
