Environmental Engineering Reference
In-Depth Information
4.6. Impact on an embankment (safety embankment)
In contrast to bounces on the slope where the fall velocities deviate and are
partially dampened on the terrain, here we are interested in the conditions that will
stop boulders on impact with an embankment perpendicular to the boulder's surface
by a boulder of a given mass
m
and velocity
v
. The dynamic force
P
and the
penetration
z
resulting from the impact are the factors determining the behavior of
the structures.
4.6.1.
Poncelet's empirical formula
This formula was established for military purposes to determine the impact of
projectiles (with velocities well above those of falling rock blocks, but with a
considerably smaller mass). It gives the penetration of the boulder:
mg
zc
=
⋅
v
m[t], v[m/s], z[cm]
[4.36]
S
where:
c: soil coefficient;
0.05 compact till;
0.10 sands and gravels;
0.20 loose soils;
S: normal section of the boulder [m
2
].
The dynamic effect (not addressed by Poncelet) is obtained by assuming the
kinetic energy of the boulder is equal to the deformation work of the soil:
2
mv
P
=
[4.37]
z
4.6.2.
Method of elastic shocks
Hertz's theory of contacts (1881) makes it possible to calculate the contact
surface and elastic deformation of two spheres with respective radii
r
1
and
r
2
under a
static load P:
