Environmental Engineering Reference
In-Depth Information
Since in different alpine regions avalanche events have been recorded over a long time
period at different sites, we can deduce the statistical properties of the
f
distribution
at different places. If the bulk friction coefficient
f
were a true physical parameter,
its statistical properties should not vary with space. Ancey thus conducted a statistical
analysis on
f
values by selecting 173 pieces of avalanche data collected from seven
sites in France. These sites are known to produce large avalanches and their activity
has been followed up since the beginning of the 20th century. Figure 2.8 shows the
probability distribution of
f
for each site together with the entire sample. Although
the curves are close and similar, they are not statistically identical. This means that
the probability distribution function of
f
is not uniquely determined and depends on
other parameters such as snow properties, site configuration, etc. Within this approach,
the Coulomb model successfully captures the flow features, but its friction parameter
is not a true physical parameter. This, however, should not negate the interest of
the Coulomb model because, given the number of approximations underpinning the
sliding-block model, the statistical deviance may originate from crude assumptions.
2.2.3.2.
Simple models for airborne avalanches
The first-generation models used the analogy of density currents along inclined
surfaces. Extending a model proposed by Ellison and Turner [ELL 59] on the motion
of an inclined plume, Hopfinger and Tochon-Danguy [HOP 77] inferred the mean
velocity of a steady current, assumed to represent the avalanche body behind the
head. They found that the front velocity of the current was fairly independent
of the bed slope. Further important theoretical contributions to modeling steady
1.75
1.5
1.25
1
0.75
0.5
0.25
0
0.2
0.4
0.6
0.8
1
f
Figure 2.8.
Empirical probability distribution functions (pdf) of the 173 f values collected
from the seven paths. The thick line represents the distribution function of the total sample,
whereas the thin lines are related to individual paths. Each curve has been split into three
parts: the central part (solid line) corresponds to the range of computed μ values, while the
end parts have been extrapolated. After Ancey [ANC 05]
