Environmental Engineering Reference
In-Depth Information
B
20
10
15
10
5
A
C
0
7
200
300
400
500
600
700
800
x(m)
B
A
5
C
1
1.5
2
3
5
7
10
15
20
u
(m/s)
Figure 2.7.
Variation in the frictional force per unit mass F/mwith the avalanche velocity u
for the avalanche of 21 December 1997 at the Arabba site (solid line); F/mwas obtained by
applying equation [2.2] to the measured velocities and path profile, both regularized using
Legendre polynomials. The dashed curve stands for the variation in the driving force per unit
mass g
sin
θ. In the inset, we have reported the variations in the measured velocities (dots)
with downstream distance x. In the inset, the solid line represents the interpolated velocities
while the dashed line stands for the velocity of a rigid body sliding in a purely Coulombic
regime (with f
=0
.
66
). Letters from A to C refer to various stages of the avalanche run (see
text). After Ancey and Meunier [ANC 04c]
velocity and was slightly lower than the gravity acceleration
g
sin
θ
. Because of the
small difference between
g
sin
θ
and
F/m
, the avalanche accelerated less vigorously
than an avalanche in an inertial regime. At instant B, the avalanche reached its
maximum velocity (24 m/s). At this point, the frictional force started exceeding
the gravitational force and the avalanche decelerated monotonically. Obviously, the
frictional force did depend on the avalanche velocity, as shown in Figure 2.4, but this
dependence remained slight since between B and C so we have:
F/m ∝ u
0
.
1
±
0
.
05
.
Thus, as a first approximation, the frictional force can be considered constant between
instants A and C:
F/m
=5
1
.
3 m/s
2
. As shown in the inset of Figure 2.7, the
calculated velocities obtained by assuming a purely Coulombic regime (dashed curve)
compare well with the data: like the recorded values, the calculated velocities show
an asymmetric U-shaped form, while the relative deviation between the two curves is
less than 20%.
±
For a few events, the bulk frictional force shows a dependence on the mean
velocity, but no clear trend in the
f
(
u
) dependence was found [ANC 04c]. An
interesting property of this simple Coulomb block model is that knowing the runout
distance (point of furthest reach) of an avalanche makes it possible to infer the
f
value.
