Environmental Engineering Reference
In-Depth Information
The module
E
of the terrain can also be defined by the usual geotechnical value:
4
1
E
M
=
( )
E
2
π
−
v
from which from [4.40] and [4.41] it follows that:
4
r
π
κ
=
=
rM
E
3
πκ
3
[4.42]
2/5
⎡
2
⎤
15
mv
1
z
==
⎢
α
⎥
22
π
rM
⎢
⎥
⎣
⎦
E
3/5
⎡
2
⎤
π
15
mv
1
3/2
Pz
=
κ
=
Mr
⎢
⎥
E
3
2
π
2
rM
⎢
⎥
⎣
⎦
E
[4.43]
3/5
2
⎛ ⎞
mv
2/5 1/5
P
=
1.765
Mr
⎜
⎜
⎝ ⎠
E
2
Equation [4.37] can also replace equation [4.42] to calculate the penetration of
the boulder starting from
P
.
4.6.3.
Dynamic punching (Habib, see [CHA 79])
By using the terms of load-bearing capacity of a foundation
N
γ
and
N
q
, the
equation for the penetration of the boulders for a spherical boulder of radius
r
is as
follows:
2
dz
()
m
=
F
z
= +
a
bz
[4.44]
2
dt
ar NS
=
γ
[4.45]
γ
bNS
=
γ
[4.46]
q
