Page 278 - Rock Mechanics For Underground Mining

EXCAVATION DESIGN IN BLOCKY ROCK

Figure 9.16 Symmetrical wedge in
the crown of a circular excavation (af-
ter Sofianos et al., 1999).

that associated with elastic joint deformability, and thereby reduce the final horizontal
force responsible for block retention in the crown of the opening.
For the particular case of a symmetrical wedge in the crown of a circular opening,
Sofianos et al. (1999) considered an opening of radius R in a deviatoric stress field
defined by p and K 0 p, with the principal stress axes oriented in the vertical and
horizontal directions. The problem geometry for a wedge of height, h, is shown in
Figure 9.16.
The problem is solved in terms of quantities similar to those above. The wedge
is acted on by its weight, W, a support force, S, and horizontal and vertical forces,
H 0 and V 0 , on the wedge surfaces. Stability is assessed in terms of the horizontal
confining force, H 0 , and the pull-out load, P 0 , the applied downward load required to
bring the wedge to limiting equilibrium.
The expression derived for H 0 is
1
H 0 = pR{(1 + K 0 )C H1 − (1 − K 0 )C H2 }
2
1
= pRC H (9.31)
2
where
h 1

C H1 = + 1 − h
R + 1
R

h 1
C H2 =
R + 1 − h + 1 3
R
C H = (1 + K 0 )C H1 − (1 − K 0 )C H2
For a vertical principal stress p given by p = z, where z is the depth below surface,
the normalized pull-out force q (given by P 0 /W) for the crown wedge is obtained
through the following expressions:

q = zC H M/(RC W ) (9.32)

260