Environmental Engineering Reference
In-Depth Information
100
80
60
40
20
0
0
500
1,000
1,500
2,000
y
f
(m)
Figure 2.10.
Dependence of the front velocity on the erodible mass. Solid line:
ρ
s
h
n
= 105
kg/m
2
; dashed line: ρ
s
h
n
=50
kg/m
2
; long-dashed line: ρ
s
h
n
= 150
kg/m
2
.
After [ANC 04a]
(
y
= 1250m) we have considered that on average the released snow layer
h
n
is 0.7
m thick and is entirely entrained into the avalanche. Using
α
v
∝ Ri
−
1
for
Ri
1
1,
α
v
=
e
−
1
.
6
Ri
2
while for
[FER 91], we apply the following relationship: for
Ri ≤
Ri >
1, we take
α
v
=0
.
2
/Ri
.
As shown in Figure 2.10, the avalanche accelerated vigorously after the release and
reached velocities as high as 80 m/s. The velocity variation in the release phase is fairly
well described by the KSB model. The model predicts a bell-shaped velocity variation
while field data provide a flatter velocity variation. The calculated flow depth at
z
=
1640m is approximately 60m which is consistent with the value estimated from the
video tapes. To evaluate the sensitivity of the simulation results, we examined different
values of the erodible mass. In Figure 2.10, we have reported the comparison between
field data and computations made with three different assumptions:
ρ
s
h
n
=50, 105,
or 150 kg/m
2
. It can be seen that there is no significant variation in the calculated
velocities in the accelerating phase, but both the maximum velocity and the position
at which the maximum velocity is reached depend on the
ρ
s
h
n
value. By increasing
the erodible mass per unit surface from 50 to 150 kg/m
2
, the maximum velocity is
increased from 69 to 105 m/s, i.e. by a factor of 1.5. Note that the dependence of the
maximum velocity on the snowcover thickness is consistent with field measurements
made by Dufour
et al.
[DUF 01]: for instance, the avalanche of 10 February 1999
was approximately half as large in terms of deposited volume as the avalanche of 25
February 1999, and its maximum velocity was 25% lower than the maximum velocity
recorded on 25 February 1999. This result is of great importance in engineering
applications since it means that the maximum velocity and, thereby, the destructive
power of a powder-snow avalanche mainly result from the ability to entrain snow
from the snowcover when the avalanche descends.
