Environmental Engineering Reference
In-Depth Information
For the continuation of the calculation, the greater of the two forces found will
be selected. This iterative method makes it possible to verify the stability of the final
block downstream and to determine the load
T
to be applied to it, if necessary.
4.3. Contact-impact
4.3.1.
General remarks
The impact of a boulder on rocky or unconsolidated strata brings into play
complex phenomena based on the theory of inelastic shocks and contact forces
(static and dynamic friction, rolling with and without sliding). In addition, high
dynamic forces mobilize the plasticity of the terrain and the normal coefficient of
restitution at the surface varies with the mass of the impacting block (boulder). The
theory of plastic shocks remains to be established in geotechnics. Nonetheless, a few
primary mechanisms can be defined.
4.3.2.
Impact at the surface of the terrain
Let us assume that the toppling of a block with a mass
m
detaching itself from a
cliff gives it an angular rotation speed ω
.
After a fall of height
h
above the terrain of
impact, the vertical velocity is equal to
v
=
2
gh
, only taking gravity into account
and neglecting air resistance.
The kinetic energy of the block includes a translation term and a rotation term:
2
2
mv
J
ω
E
=
+
( : inertia moment of the block)
J
[4.10]
2
2
By breaking the velocity down into two terms − one normal, the other
perpendicular to the surface of impact of inclination β (see Figure 4.6) − just before
the shock we obtain the following components, given a (-) sign:
−
⎤
v
=−
v
cos
β
n
⎥
⎥
−
vv
=
sin
β
[4.11]
t
⎥
⎥
−
ωω
=
⎦
During the shock, part of the kinetic energy is dissipated plastically, with a
normal coefficient of restitution
e
n
<1 tangential coefficient of restitution
e
t
= 1 if the
