Instability of Rock Masses - Environmental Geomechanics - page 109

4.7. Capacity of the protective structures

4.7.1. Elastoplastic model

The kinetic energy of impact must be absorbed by the deformation work of the
structural element of mass M by using its plastic deformation capacity [TON 88],
see Figure 4.11.

Initial energy:

2
0

mv

E = (boulder)

2

Energy of the system “boulder + element” after impact (soft shock):

( )

mv =+ m M v

1 . 0

1

( )

mMv +

E

E = = [4.48]

ext

( )

2 Mm / + 1

Internal deformation energy:

y

⎛ ⎞

el

EPy = −

⎠

[4.49]

⎜ ⎟

int u u

2

⎝

where:

P u : ultimate load of the element;
y u : plastic deformation;
y el : elastic deformation.

The equality of energies gives:

0

y mv

⎛ ⎞

el

Py − = [4.50]

⎜ ⎟

uu

( )

2

2 ⎡ Mm / + 1 ⎤

⎝ ⎠ ⎣

⎦