Page 281 - Rock Mechanics For Underground Mining

DESIGN PRACTICE IN BLOCKY ROCK

and the x, y, z components of the shear resistance on any face can be determined
directly from its magnitude and the components of the appropriate unit vector for
the face, defined by equation 9.34. Taking account of all applied normal forces and
mobilised shear resistances, the net vertical force associated with the internal surface
forces is

3

F z = N i (b zi tan i + a zi ) (9.35)
i=1
Introducing the weight of the wedge, if the resultant vertical force satisfies the con-
dition

F z + W < 0 (9.36)

the wedge is potentially stable under the set of surface and body forces. An added
condition to be satisfied in this assessment is that the sum of each pair of terms on
the right-hand side of equation 9.35, i.e. (b z tan + a z ), must be negative. If the sum
of any such pair of terms is positive, this implies that the particular surface will be
subject to slip under the prevailing state of stress. In such a case, the initiation of
slip must be anticipated to lead to expansion of the area of slip over the other block
surfaces, and subsequent detachment of the wedge from the crown of the opening.
The case considered above concerned potential displacement of the wedge in the
vertical direction. For particular joint attitudes, the kinematically possible displace-
ment may be parallel to the dip vector of a plane of weakness, or parallel to the line
of intersection of two planes. In these cases, some simple modifications are required
to the above analysis. Since, in all cases, the lines of action of the maximum shear
resistances are subparallel to the direction of displacement, equations 9.35 and 9.36
should be developed by considering the direction of the feasible displacement as the
reference direction. This merely involves dot products of the various operating forces
with a unit vector in the reference direction.
As noted earlier, the type of analysis outlined above can be conducted readily with
appropriate computer codes. They are available from several suppliers, and take due
account of rock structure, excavation geometry, local state of stress, and rock support
and reinforcement.

9.5 Design practice in blocky rock

In the course of considering the behaviour of rock prisms and wedges in the periphery
of underground excavations, it was seen that, once a kinematically feasible collapse
mode exists, the stability of the system depends on:
(a) the tractions on the joint-defined surfaces of the block, and therefore on the final
state of stress around the excavation and the attitudes of the joints;
(b) the frictional properties of the joints;
(c) the weight of the prism, i.e. its volume and unit weight.
Effective excavation design in a jointed rock mass requires a general understanding
of the engineering significance of each of these factors.
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