Engineering Rock Mechanics

Stabihzation of 'transitional' rock masses 28 1

instability 'f p' will ./, 2

&,change as $i changes /&

Figure 16.12 The use of the
@,=20" and (b) q3=50".

construction for a non-circular opening with (a)

The analysis as presented assumes that the normal to the discontinuities
is in the plane of the cross-section. If this is not the case then the angle project-
ed onto the plane of the cross-section will be an 'apparent 4;. This angle can
conveniently be determined using hemispherical projection methods.
Considering the case when a support pressure is applied normal to the
excavation boundary, it is possible to calculate the pressure required to
inhibit inter-layer slip. In the plane of the cross-section, the stresses acting
on an element of material immediately adjacent to the boundary are 00 and
p, as shown in Fig. 16.13. Application of the stress transformation
equations and utilization of the Mohr-Coulomb failure criterion results in
the following expression for the required support pressure:

P=o0 tan(a - $1 (p, < a < 90.

tan a

In general, the tangential stress 00 will vary around the boundary. For
simple geometries, closed-form solutions exist for the tangential stress,
but for more complex shapes a numerical procedure is adopted.

vJ''F pressure Support

P

Figure 16.13 The 4, theory applied to the calculation of support pressure.